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Convolution with the Inverse FFT of a Box Filter

It's just a scaling factor that you have been inconsistent with, as you suspect. To make the two approaches match, either get rid of the following line or multiply your fft approach by ...
Stephen's user avatar
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CZT: Do Bluestein algorithm perform backward transformation?

Reversing the sign of the exponent in the CZT only results in the inverse CZT for transforms on the unit circle ($A_0 = 1$ and $W_0 = 1$).1 This is noted in the actual ICZT paper cited by the OP. For ...
Gillespie's user avatar
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1 vote

Phase shift between X and Y components of the same wave

From the OP's plot we can clearly see the quadrature relationship between the signals: I don't recommend using the FFT to extract phase vs time, as we can get that more directly from the scaled ...
Dan Boschen's user avatar
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1 vote

Phase shift between X and Y components of the same wave

These are narrow band signals. The phase at most frequencies that are outside of the band are undefined or dominated by noise. You need to evaluate the phase difference at the exact center frequency ...
Hilmar's user avatar
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1 vote
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Is the analytical fourier transform of an exponential decay the same as the FFT of a time series of the same signal?

The main problem here is that you want to evaluate the transfer functions over a complex plane. For continuous systems that's typically done using the Laplace Transform and for discrete systems you ...
Hilmar's user avatar
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1 vote

Finding a certain animal from wildlife audio

Template matching is deemed a classical approach to attack this problem. An alternative state-of-the-art method is to use deep learning (CNN) classifier given your data is labeled. However, if you ...
AHT's user avatar
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1 vote
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How to do spectral averaging to get satisfactory results?

The following line in your code is incorrect for setting the phase: ...
Stephen's user avatar
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0 votes

Is it possible to transform a pointwise product into a convolution?

Here is a solution that doesn't require the vectors $A$ and $B$ have a certain structure, which ends up being the reverse of what you did: $$G=\mathcal F^{-1}\left\{\frac{\mathcal F\{AB\}}{\mathcal F\{...
Stephen's user avatar
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1 vote

How single-tap equalization can be performed in OFDM for perfect channel estimation?

If I have for example IFFT length of 3 with cyclic prefix length of 2 and 3 channel taps, how can I illustrate the frequency domain equalization in OFDM? You can't! Your cyclic prefix is shorter than ...
Marcus Müller's user avatar
1 vote

Debugging a Haar wavelet transform in the Fourier domain

Just adding to Matt's answer. You can see the aliasing in the time domain wave forms. The Haar wavelet has infinite bandwidth so you can't sample it without aliasing.
Hilmar's user avatar
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2 votes
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Debugging a Haar wavelet transform in the Fourier domain

The results are different because they represent different things. The first formula is the continuous Fourier transform of the continuous Haar wavelet (apart from a scaling factor). The second result ...
Matt L.'s user avatar
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4 votes

Why zero-pad at the end of a signal?

The frequency resolution in the context of the DFT is indeed dependent on the length of the signal in the time domain, not merely the size of the DFT. Here’s a more detailed explanation: Frequency ...
AHT's user avatar
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Why zero-pad at the end of a signal?

What differences does it make? In one line - The phase information of the Fourier transform changes. Explanation: Adding zeros at the start of the signal translates to adding delay. Consider the ...
SakSath's user avatar
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2 votes
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Baseband downconversion without imaging

@moltarze Still you did not implement down conversion correctly, I think. Let $x[n] = x_r[n] + ix_i[n]$ be the input signal to be down-converted by the carrier $$c[n] = e^{-in\text{arg}} = \cos(n\...
AHT's user avatar
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1 vote

Baseband downconversion without imaging

Keep in mind that multiplying an input time-domain signal by a cosine wave (or a sine wave) is "modulation" and NOT "frequency translation." To implement frequency translation you ...
Richard Lyons's user avatar
0 votes

Inverse filtering to undo a convolution blows up

A better approach would be to apply some method to solve problems on the form $$\min_v \|Mv - d\|$$ or possibly $$\min_v \|M(v+d) - d\|$$ Where $M$ is the Gaussian convolution operation, $d$ is the ...
mathreadler's user avatar
2 votes
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ECG analysis in MATLAB

A few points to discuss IIR filter are typically minimum phase and FIR are typically linear phase. That's not always the case, but good enough for the current discussion. Linear phase filters are good ...
Hilmar's user avatar
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0 votes

Is it possible to find the FFT of a 1024-point signal by taking 8-input points at a time and calculating the FFT of those 8-points until the end?

There is a divide and conquer approach to computing the FFT detailed in this PDF. Here is an implementation as in section 8.1 ...
rtclark's user avatar
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1 vote

Linear convolution of a 100 sample time series and a 20 tap filter in the frequency domain

So the linear convolution correct length is as you say: $$ N_t + N_h - 1 $$ where $N_t$ is the length of $t$ (e.g. 100) and $N_h$ is the length of $h$ (e.g. 20). This equation: $$ {\tt FFT}^{-1} \left ...
Peter K.'s user avatar
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1 vote

Linear convolution of a 100 sample time series and a 20 tap filter in the frequency domain

I have never heard of "20 tap filter". Is that just a FIR filter with 20 coefficients? yes. (some functions for filtering make it a bit confusing what is the number of coefficients and what ...
Marcus Müller's user avatar

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