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I am using fft to plot the signal spectrum (convert real and imaginary components to amplitude values). If my signal is of odd length, I take $fft[0]$ as DC and use $fft[1;(N-1)/2)]$ values to get the amplitudes of the harmonics (from 1 Hz to (N-1)/2 Hz). But if my signal is of even length, the $fft$ element with index...
There is a very useful tool in my DAW which allows me to isolate groups of "loudness" within the frequency domain. Basically, any bin greater than some min, less than some max. It makes it easy to boost fundamentals, or bring out secondary harmonics; both things which are largely defined by how loud they sound. This ...
I want to analyze vibrations and I am new to signal processing and I have many doubts, I use an accelerometer and FFT for this. First, I don't know what frequencies to check and as a result, I don't know with what frequency sampling should be done. ---> I am sampling with a frequency of 400 Hz. I don't know if it is co...
So I am developing a signal processing algorithm to classify in real time depending on how many peaks I have in my time series, in a delta. I implemented a circular buffer and accumulator to keep in memory the number of peaks in that buffer. However, it seems like for some reason, my accumulator reduces drastically whe...
For example if I have the following transfer function: $$H(s) = \frac{1}{\cosh(\sqrt{s/10})}$$ Can I do the bode plot it in matlab or do I need to rationalize it beforehand?
So we are given a block diagram and we have to find the y[n] "equation". The problem is i just dont get what that plus at the end does Also i have "calculated" the equation but id like to see if its correct or not what i found out is: $x[n]z^{-1}+x[n]z^{-2}a+y[n]z^{-2}c+y[n]z^{-1}b=y[n]$ Is this correct? Also does tha...
I'm searching for a way to parse a signal that mixes multiple square waves of different frequencies. The intended output is the frequency of each of the mixed square waves. This answer provides an example of mixing signals, he uses OR gate as an example, but we could change to a more appropriate one if needed (as to hi...
In my previous question I use a system identification case as an example. Here I came across another question. I want to design a FIR filter of length $L$ to equalize an LTI system whose impulse response is $h(n)$ of length $N$, and my target response is $d(n)$ which is maybe a delayed $\delta(n-D)$. The problem can be...
I am trying to implement the Belief Propagation (Sum-product algorithm) to decode LDPC codes in Matlab. I have implemented the equations correctly and did a comparison between my implementation and the provided implementation in Matlab. For some reason my implementation floors at BER = $10^{-2}$. I suspect that this is...
Student here, As an academic exercise, is the system $$y[n] = x[n-1]x[2n]$$ Invertible? I thought it was since you could find an infinite multiplication series for y[n] that allows you to recover x. Could someone go over exactly what one to one would mean for a function from X*X->Y? I have only learned one to one funct...
Offset Quadrature Phase Shift Keying (OQPSK) like QPSK transmits two bits per symbol. However, because of the offset on the quadrature component there are two transitions per symbol. Does this not double the bandwidth of each symbol, leading OQPSK to be more similar to BPSK in terms of spectral efficiency? This would m...
I am looking for a good algorithm or a tool to compare two spectrogram outputs for unit testing. I can visually confirm the outputs are similar but I would like to automate this process. The basic stats of the outputs, such as min/max/avg/median are kind of the same but this would not catch true differences.
\begin{eqnarray} X_k &=& F X_{k-1}+ \omega_k \nonumber \\ Z_k &=& H X_k + \nu_k \end{eqnarray} The first equation is state exploration equation and second one measurement equation. Point to be noted, I dont have $Bu$ term in my state equation unlike common state exploration equation. Here, I was trying to gen...
I understand the theory of amplitude modulation. However, I couldn't understand it's implementation in SDR, which use IQ data, and I would like to learn end to end amplitude modulation system in detail as mathematical model in discrete time. Let say we want to transmit wav file and assume that each sample of the wav fi...
I have a sensor placed on vibration aggregate. When the aggregate is not working, my sensor produces some noise signal. So when my aggregate is working, my sensor produces "result" signal which is the sum of the vibration signal and the noise signal. I want to extract only the vibration (clean) signal from "result" sig...
I am working with BladeRF xA4. I have a signal generator at 1.5GHz modulated with cos(2pif_mt)+jsin(2pif_m*t). This generator is conected to a signal splitter. Next to the splitter two cables are connected to two inputs of the BladeRF. I acquired the waves with: status = bladerf_sync_rx(dev_, &arr_, READ_SAMPLE_SIZE, ...
I am trying to control a plant with PID using tuning rules such as the Ziegler-Nichols rules. However, it is not always easy just to send a step to your plant source of the image. Another method to find the same parameters is to set your plant on the verge of instability and measure the gain and pulsation of the oscill...
I have the task to find a transition that fulfills the first Nyquist Criterion. After that I am supposed to match that filter to an AWGN channel. For the first part I thought a raised cosine transition in the frequency domain should be a good start. But now, I don’t know how to match that filter to an AWGN channel in t...
I would like to analyse a wav audio file and determine the key passages of the song using python. To do this, I have so far first analysed the root mean square and then formed the derivative, which leads to an array with around 15000 values. I thought that I could determine the key points by finding the values of the a...
I have seen a number of answers on various forums for why we need to scale the magnitude of DFT output by 2 (e.g. 1) to account for discarding negative frequencies, or 2) due to the 2 in the denominator of the exponential form of sine and cosine). However, as far as I can tell these are not the root reason for this, an...
I’m working on a image signal project using C++ with DFT, IDEF. I major in physics and have lots of experience dealing with 1d fourier transform.. HOWEVER, 2d dft is really not intuitive. I studied a lot and now have a little understanding of what is 2d dft. THIS IS WHAT I REALLY WANT TO KNOW. In 1d, assume you have 2 ...
I am trying to build a filter for the detection of signals with the known form in noisy and low-amplitude data. I used a simple example in Python provided here: https://www.youtube.com/watch?v=XXLV9g6RQQ4 but for the data I have. initial_signal is a numpy array, it has length of 8000 points. (for each element of initia...
With amplitude modulation the signal only has a real component and the modulated signal has two sidebands that are symmetric around the carrier frequency. My understanding is that in QAM the sidebands are necessarily not symmetric. The point of confusion for me is that QAM is effectively just two separate signals ampli...
Background I was working through a DSP MOOC in the evenings and was presented with a question regarding the Fourier basis functions. Initially I tried to test my hypothesis with the quick python script below however, this did not produce the answer I was expecting (the accumulated total should be approximately equal t...
For 3 phase shifted sine waves using the projected pattern: I = sin(x + δi) where δ ∈ [-2pi/3, 0, +2pi/3] which is then projected onto a scene. The resulting image is captured with a camera. I am using the method mentioned below as Robust sine patterns: I have the following questions: From what I understand, phi (obt...
I am following the instructions of this paper (https://www.earthdoc.org/content/journals/10.3997/1873-0604.2003015) to process a ground-penetrating radar (GPR) signal (a discrete signal sampled at a fixed rate). The main issue here is that the source signal of the GPR is unknown. So if a can deconvolute an estimated so...
I tried solving a test question that frankly stumped me. If you could explain to me the solution I’d be really grateful. Given $a, b \in \mathcal{R}$ the system $R_v$ takes the complex input $a + bj$ and returns $a + bvj$. For which values of v the system is linear? This system accepts both discrete and continuous in...
I'm doing some control system work. I was shocked* -- shocked to learn that while Scipy has some nice linear systems classes, they don't extend to computing the cascades or paralleling of two systems. I.e., in Scilab if you have system H and system G, you can express their parallel as HpG = H + G, or their cascade as ...
I am generating two signals of same frequency, i introduce a fixed delay in one of the signal and then try to find out the simulated delay using MATLAB 'gccphat' and 'finddelay' functions, but not able to measure correct delay. MATLAB Code script is given below: clc clear close all %%%%===========================...
Sinc is $\propto 1/t$. If $x(t)$ is bounded, then there exists $t: |x(t)/t| < \epsilon_M$, where $\epsilon_M$ is machine epsilon. If $x(t)$ is also time-limited, it also means there's $\tau$ such that $\int_{-\infty}^{\infty} |x(t) \text{sinc}(t - \tau)| dt < \epsilon_M$ (i.e. sinc eventually decays enough), meaning $...
I am learning resampling theory, and for the time being I am specifically interested in downsampling. I have a textbook that is not a dsp textbook but has a section on resampling. The way they put it, resampling has three steps: Rebuild the analog signal, LPF it, then resample at the new rate. So the equivalent of: DAC...
I was trying to simulate data for a 2 pole low pass filter inorder to solve with kalman filter to estimate the true states. With the below code I was unable to generate true states that look like sin function. I took x(t) = A0sin(wct) with wc = 2pi*fc, fc is cutoff frequency. Can some one help me regarding this? I am t...
In the "Introduction tu Bluetooth Device Testing" document ( https://download.ni.com/evaluation/rf/intro_to_bluetooth_test.pdf ), the modulations for Bluetooth Classic are said to be a Binary GFSK at 1 Msymbol/s, a pi/4-DQPSK at 2Msymbol/s, and a 8DPSK at 3Msymbol/s. But the phy data rates for the packets are said to b...
From what I understand FIR filter order is same as it's group delay because of the linear phase and every frequency being delayed by same amount. For IIR filter, filter order only tells that filter needs that number of past samples to compute a new value. But IIR filter order doesn't translate to output delay or group ...
On page 137 of "Understanding Digital Signal Processing" by R.G. Lyons I found that if I separate the standard DFT form: $$X(m)=\sum_{n=0}^{N-1}x(n)e^{-j2\pi nm/N}\tag{4-11}$$ by odd and even components, with $W_{N}^{nm} = e^{-j(2\pi/N) mn}$: $$X(m)=\sum_{n=0}^{(N/2)-1}x(2n)W_{N/2}^{nm}+W_{N}^m\sum_{n=0}^{(N/2)-1}x(...
In a discrete-time difference equation (ARX model), the output $y[k]$ is dependent on its past values and inputs, expressed as: $y[k] = -a_1 y[k-1] - ... - a_N y[k-N] + b_1 u[k-1] + ... + b_M u[k-M]$, with $N \geq M$. However, when converting the system to an equivalent state-space form, such as the controller canonica...
I am investigating the properties of the cascaded integrator comb (CIC) filter (for a $\Sigma\Delta$-modulator). I have two questions: What's the correct method to design a fast settling decimation filter, is the combination of SINC3+SINC1 in the right direction? or any other topology? (narow bandwidth LPF, decimation...
I would like mention my understanding in the following, In an LTE OFDM signal assume, Nfft=8; scs=15 kHz; BW=5MHz; Sampling Rate N=7.68 MHz; We are taking 1msec of sample; Therefore total sample =76800 sample. I found a model from Mathworks which is explained on this link. txWaveform={76800} % Assume OFDM Signal ...
is anyone could help understand this 50/60Hz rejection filter? The basic information: Fs=1MHz, DOR(data output rate)=25SPS, with both 50Hz & 60Hz rejeciton, settling within 1 cycle, 1/DOR. The simplified sturcture: SINC5 + SINC1 + 50/60Hz-Rejection. So how to relize it? What I know is that the SINC5's DOR=31.25KHz, OS...
In optical OFDM systems, called DCO-OFDM, we usually use the data with its flipped complex conjugate to produce real time-domain signal while the first and $N/2 +1$ subcarriers are kept null, $N$ is the number of subcarriers in each OFDM symbol (time-domain signal is the data resulted of multiplication with inverse fa...
I am working on the following problem: I have a solution that I am pretty confident is correct as have checked the output in python. However, it is long and the entire time I was answering the question I felt like I am missing an obvious, easier approach. Is there a better way to do this? Solution: The approach taken ...
I am recording some data for scientific purposes (it is neurological data), and the data is corrupted by some very strange noise. At multiples of about 700 Hz (slightly differing on different days) there are box like peaks in the multitaper spectrum. The width of each box is proportional to its frequency. The highest p...
I have a question regarding Recursive Least Squares (RLS) adaptive filter. According to Wikipedia (Recursive Least Squares in Wikipedia), to prevent infinite memory one introduces a forgetting factor $0 < \lambda \le 1$. Then the RLS recursive update equations are: The relevant update is: $$ \mathbf{P}(n) = \lambda^{-...
Edit: from Wikipedia's Delta-sigma modulation it looks like since the microphone basically is an ADC, and that as such mics with PDM output may use a Σ‑Δ modulator internally. Also, from Selecting PDM Microphone Clock Frequencies and Decimation Ratios I read that "A Pulse Density Modulation (PDM) microphone uses a Sigm...
I have group of .wav files that contains human speech (same person). Each file is 2-3 second long. Now, I'm creating one long file (lets say all.wav) that contains all files mentioned above. Basically, all files are concatenated together, like this: |--file1--|--file2--|--file3--|...|--fileN--| There are about 100 file...
I want to know what the sample rate of I and Q samples generated for transmission, in the function below from https://github.com/lyusupov/ADSB-Out/blob/master/ADSB_Encoder.py samples are generated for transmission by a SDR (HackRF) so they are aligned to 256k buffer (HackRF requirement) and then SDR (HackRF) commanded...
I'm really new to signal processing research. I'm trying to replicate Kirill Kochetov and Andrey Filchenkov. 2021. Generative Adversarial Networks for Respiratory Sound Augmentation. In Proceedings of the 2020 1st International Conference on Control, Robotics and Intelligent System (CCRIS '20). Association for Computi...
I am trying to do a Fourier Transform and Inverse Fourier Transform. The problem is that I am not getting the original signal after inverse transform. # set signal and transform constants samples = 10000 t = np.arange(samples) cf = 1000 # carrier frequency Hz mf = 60 # modulation frequency Hz # signal is a classic AM ...
I have a huge dataset, way too much to be loaded into memory. I need to downsample the data to a new rate. Normally, this would consist of upsampling by N, applying FIR LPF, then decimating by M to achieve the new sampling rate N/M. An important point here is that with this method, your first sample of the input will c...
I'm trying to simulate frequency demodulation in Python. As a part of this, I'm implementing a band-pass filter with cutoff frequencies at $f_c-2f_m$ and $f_c+2f_m$. There is frequency shift in the final frequency response after passing through the band-pass filter. Is there any specific reason why? I'm reading the aud...
I am trying to write a Matlab code to produce motion and Gaussian blur. Here is my code: f0=imread('cameraman.png'); [Nx,Ny,Nz]=size(f0); if Nz>1;f0=double(rgb2gray(f0)); else f0=double(f0); end blurfilter1 = fspecial('gaussian', [7 7], 1); blurfilter2 = fspecial('motion',5,30); Au = @(u) imfilter(u,blurfilte...
I have been asked to prove the following; Show that a sinusoid of amplitude 10V and frequency 2kHz sampled at %fs = 10kHz is an alias of a 500Hz sampled signal. I have develped the code for the 500hz sample V= 10; Fs = 10000; % Sampling frequency = 10 kHz t = [1:1:10]/Fs; % Constructs a time array t with 10 samples y=...
I am trying to understand how a SIM7600G 4G modem degrades the audio when configured for 8 kHz sampling rate. I created a reference audio using librosa.chirp to slowly sine sweep from 30 Hz to 3400 Hz. I saved the raw audio using 8 kHz sampling rate. Then I called the modem from a high quality digital land line and re...
I know that if I have a closed-form algebraic expression $X(z)$ and I specify the region of convergence, this uniquely identifies exactly time-domain sequence (inverse Z-transform) $x[n]$. Let's suppose I have a pole-zero plot specifying that $X(z)$ has a single zero at $z=-1$ and four poles at $z=1/2, 2, 3,$ and $4$ (...
Edited for conciseness, please see below: Question: How does overlap and save work, in the context of array buffers? How does overlap and add work? For a specific use case involving STFT, which one is better? Does either return more correct results? My attempts to read about it generally lead to confusion. I cannot rea...
I have a MATLAB code in which I need to calculate the SNR and SINAD of received signal at known frequency (assumed as tone signal). The issue is that sometimes the power at that frequency is lower than some of the spurs and distortion elements which may or may not have any relation at my desired frequency and the way t...
I was trying to write 4QPSK in Python for my self learning based on the book Digital Modulations Using Python. When I have my sampling frequency set to 4 times the carrier frequency, I get exactly 4 points in the eye diagram using the inphase and quadrature values. Also I get only 4 unique phases with modulated complex...
On Wikipedia, I came across the following equation $$h[n] = Th_c(nT)$$ This equation relates the impulse response of the discrete time filter which is the impulse invariant of a continuous time filter. $h_c(t)$ denotes the impulse response of the continuous time filter, $h[n]$ denotes the discrete time filter. I fail t...
I have a - perhaps naive - question regarding the quantization noise/error. Assuming the goal is not the performance of the quantizer but rather being able to model the quantization noise exactly - say, Gaussian with certain mean and variance - are there any methods that would let one achieve this? There are no assumpt...
I wanted to get a Fourier transform on the stm32 MCU With the help of cmsis functions But I encountered the problem of lack of memory while the buffer size was small. After a lot of trouble, by checking the map file, I realized that a function consumes a lot of memory when called, about 150 KB. arm_rfft_fast_init_f32()...
Bit over my head in math here I want to do a notch filter in real-time programmation with codesys (the structure text here look alot like C) so I have this: Linear phase Notch filter / Band reject filter implementation in C++ and this: http://www.dspguide.com/ch19/3.htm as reference which looks like lR := 1 - 3 * lrBan...
I am trying to use matched filters for signal detection and advanced processing - to get additional information from the signal after the convolution with various templates. The task I have is pretty simple - to find patterns with known forms in the signal I have as an input - but I need to be able to distinguish the r...
I am trying to generate a pulse of the shape with the following parameters. Carrier frequency is 5 [GHz] Pulse Repetition Interval is 1600 [ns] Pulse Width is 100 [ns] Rise Time is 8 ns Fall Time is 8 ns Raised Cosine window How can I generate that pulse?
from a course in signal processing, I know some radio propagation models such as Free-space path loss, Okumura model, Hata model, and COST Hata model. They applied to a range of frequencies for up to 2 GHz. 5g/6G frequency range is more than 2 GHz, 6G is THzband What model do you use to describe 5G and 6G propagation l...
Suppose you have captured IQ data from a PSK modulated signal with intermittent blanks between signal transmission as shown in the figure below. I want to be able to automate and run an algorithm on a multitude of data captures like this to determine the phase offset and then plot the Phase corrected like the figure b...
I am currently modeling FMCW (linear FM) and SFCW (stepped FM) chirps in python. For my project, I need to simulate those signals as a transmit chirp and a received one, scattered from point targets at some distance. I think I got it generally right for the linear chirps, where I am generating the transmit signal like ...
The implementations of Synchrosqueezing wavelet transform in Python (ssqueezepy) and MATLAB both write in their documentation that they implement the synchrosqueezing algorithm on the Continuous Wavelet Transform. However, these functions take in discrete-time input and return discrete frequency/scale output. It is m...
I consider values physical measurements, expressed as variables of type int16, uint32, float or other. I consider a Gaussian model for measurements, i.e. I have estimates for the mean and standard deviation values. The measurements are sent through a communication channel, which may introduce errors. I wish to "flag" u...
I'm dealing with the following question : The system realizes an accumulator, therefore its impulse response (h[n]) is just the unit step function multiplied by some factor . In the next subsections , I'm asked to provide an answer in terms of X(ejw ) meaning I have to assume that the system is stable but it is obvio...
I'm completely new to the world of audio and signals. I noticed that when I opened Audacity and generated one second of silence (details below) and converted the raw WAVE file to a list of integers, that the silence wasn't a bunch of zeroes. (Yes, I was sure to convert the endianness.) It was a series of seemingly rand...
I am struggling with implementing FM demodulation for IQ samples that has 0 center frequency from RTL-SDR ... I have found the following algorithm for FM demodulation, see FM demodulation: analytic_signal = scipy.signal.hilbert(vfo_channel_fm.real) baseband = analytic_signal demod_channel = np.angle(baseband[1::1] * np...
I'm trying to recover amplitude/magnitude from an audio stream. I'm using FFT to go from time domain to frequency. If I feed in a signal of known amplitude, the results I get from either windowing or using scipy.signal.stft are lower than what is being fed in. I wonder if this is inherent to using a window, or if I'm j...
I have simple sine wave as input $x(t) = \sin(6\pi t)$ and then take a Fourier transform of the signal. Afterwards, I multiply that to a transfer function. I see a discontinuity 3GHz. Is this just an artifact? $ Y(\omega) = G(\omega)\cdot X(\omega) $ where $G(\omega) = \frac{-j\omega}{\omega_m^2(1+j\eta) - \omega^2}$
I have found this piece of code in Infenion DSP Library (asm code): Fir_Blk_16() ... ;(ACC)=(ACC)+h(i)*x(n-i)<<1 as comment I don't understand why the result is shifted (<<1)? Is this for rounding purposes? Thank you in advance, Anton
I have a waveform where I sliced the flat top so I can do some analysis on the amplitudes of each frequency. I have a dataset of N measurements each with M samples of current (A) over time (microseconds). I expect that there is a frequency on the 100 Hz sideband of the expected frequency. I curve fitted the expected fr...
I want to estimate the power spectrum of a given signal using Bartlett's method. I understand the general purpose of the method. However, I do not get my head around the algorithmic description of the method given in the Wikipedia article. The part I am stumbling over, is in the 2nd step: For each segment, compute the...
I have done a power spectrum density estimate using Bartlett's method. However, I was wondering if it is also possible to get a sense of the variation of the averaged spectra. Unfortunately, I have not found a method for this problem, so any reference is most welcome! I have plotted the mean and std of the DFT amplitud...
I have couple of analog synthesizers and I want to turn their oscillators into code. I've been reading about how to do it for a while and making a lookup table seems just right for me. I've been modeling some linear/nonlinear effect units, but I'm new to modeling synthesizers, so at this point, there is a great possibi...
I am very new to Kalman filter. I am doing a project using one sensor the track the sensor's position. I developed 2 methods to solve the position, one in better accuracy and one is less accurate. I would like to know that can I use Kalman filter to fuse the 2 position-solving algorithms to achieve a better performance...
I have done a power spectrum density estimate using Bartlett's method. However, I was wondering if it is also possible to get a sense of the variation of the averaged spectra. I have plotted the mean and std of the DFT amplitudes (no normalisation), which at least does not look completely off. However, when I plot the...
I just started a while ago with DSP and slowly staring to understand the concept of I/Q and what it means. I successfully could decode some bfsk, bpsk and wanted to move to msk which as not easy to understand. Lost of blog posts explain very well how to deal with as OSQSK or CPFSK. In those posts we always work with I/...
My question is: after upsampling a signal, does the output signal contain the original signal values? The diagrams I saw so far (on wikipedia and different forums) have always shown the original values but when I convolute with the fir filter coefficients, the output signal doesn't contain the original values or not al...
I am struggling to understand the meaning of the covariance of PSD (Power Spectral Density) between two frequency points ($f_1$ and $f_2$). The covariance of a function $s(t)$ in time domain $t$ is a Fourier dual of the power spectral density and that is understandable. However, in some papers, the covariance of the po...
I am trying to bandpass filter an EEG signal, nothing fancy but it's coming out pretty distorted. EEG data is taken from forehead. Sampling rate is 250 Hz. Cutoff is 2.5 Hz & 120 Hz. Tried in both matlab & python, getting same results. Matlab code: data = load("rawdata.mat"); data = data.data; figure bandpass(data,[2.5...
I have a sample of a signal lets say 8 values of a 16 value sequence. I am trying to obtain the full DFT from the partial. I am thinking that I am going to work back, I read the matlab documentation and have come acrosss an inverse function. Am I on the right track? I was not able to see a pattern in the results.. yt =...
Sorry if this is a trivial question, but I am not doing signal processing everyday. I will try to express what I think I have understood as best as possible. Suppose I apply a (linear) sweep signal to a system (like a loudspeaker in a room) and measure the response. To the input and output of that measurement I apply a...
So I am trying to understand the scattering transform on graphs (GST). There are many formulations but I am stuck on equation 8 in this paper. Here they give a condition on a wavelets that looks like Equation 10 on page 7 of Mallat's foundational paper,and claim that this means that the wavelets were derived from a mul...
When reading about SIFT I read halving resolution is the same as increasing $\sigma$ of the gaussian in terms of feature detection but reducing resolution has the advantage of reducing processing. What I am curious about is suppose we keep the image the same size and only modify $\sigma$ and apply DOG as usual. When a ...
Say I have a signal x(n) and I want to resample from rate 30Hz to 20Hz. In Matlab, I can make a filter with: fs1 = 30; fs2 = 20; f = [0 6 7 fs2/2]/(fs2/2); a = [1 1 0 0]; n = 31; b = firpm(n, f, a); This way my cutoff frequency is 7Hz. Now I want to use this as my interpolation filter. I can run x2 = resample...
What can be recommended as challenging tests for cross-fading/mixing of music? I am looking for examples of music-titles that exhibit severe volume dips when cross-faded or mixed. Ideally answers should provide pairs of (free) music-titles and the length of the cross-fading interval and also other information that is n...
I am very confused about how to write the likelihood of the following function. I have tried one and it doesn't have a maximum at the point where it should contain a maximum. The formulation of the measurement looks like this. $$ Z_m(\omega) = F(\omega, \Theta) + \eta_m(\omega) $$ Here there are many $\omega$ points w...
I'm trying to detect rapid changes in a one-dimensional signal say $[0,1]\ni t \mapsto f(t) \in [-1,1]$. By rapid changes, I mean corner points, edges, or sharp transitions at a point for example the signal switches from a value $-1$ to $+1$ on a point. For this, I'm using the STFT i.e., the Short-Time Fourier transfor...
I would like to do regression thus I need to know if my input data are noisy. In this case, I generate accelerometer data [x, y, z] from the sensor. I have a look at RMS noise, SNR etc, but I couldn't understand, which one to use to decide if data are noisy. Let's say I have some RMS noise values, but when exactly do w...
I have heard many different types of beeps, chimes, and other tones. Audacity allows me to generate simple waveforms like sine waves and square waves, as well as DTMF tones. But I want to generate tones that are like ones I've heard before but don't know the name, if they have specific names. The tones must be the sum ...
Suppose we are working with a multi resolution analysis (MRA) of $L^2(\mathbb{R})$ and let $\phi$ be the corresponding scaling function and $\psi$ the derived wavelets. Using standard notation with $\hat{f}$ denoting a Fourier transform of a function $f\in L^2(\mathbb{R})$ is it always true for all integer scales $J$ t...
I am looking clarification that I have the appropriate solution to this question, thoughts and tips to improve my understanding are also welcome! f(n) is a discrete sample of the following signal. The sample rate is $4$ Hz and the time period is from $0 - \frac{3}{4}$ $$ f(t) = 5+2\cos(2\pi t - \pi/2)+ 3\cos(4\pi t)$...
So, I'm reading Steven Brunton's book, "Data Driven Science & Engineering", and I'm trying to understand what he means by mode in this following excerpt: Most natural signals, such as images and audio, are highly compressible. This compressibility means that when the signal is written in an appropriate basis only a fe...
Given the acceleration response time history of a multi-story structure, how can I find natural frequencies using time-frequency analysis techniques? If you just provide some references or articles, I truly appreciate it.
I want to calculate the filter coefficients for both bandpass and bandstop filter for 2nd order Butterworth filter, like def low_pass_coeff(N: int, cutoff: int, samp_rate: int) -> tuple: ''' N - order of the filter cutoff - cutoff frequency (in HZ) samp_rate - sampling rate of the signal ''' ...
In this related post: https://dsp.stackexchange.com/a/86776/21048 I have demonstrated the similarity of FIR filters and their related frequency response to antenna arrays and their beam patterns (replace time with space). I also included a link describing other “super-resolution” techniques that can be used with phased...