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An increased sample rate requires proportionally longer filters (both IIR, FIR, and FFT) for the same filter transition widths, flatness, and stop band attenuation. IIR or recursive filters will also become more sensitive to numerical noise (quantization, rounding, etc.) I suggest increasing the length of all your filter kernels and implementation sizes ...


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Synchrosqueezing with ssqueezepy. from ssqueezepy import TestSignals, ssq_cwt from ssqueezepy.visuals import plot, imshow x = TestSignals(N=2048).lchirp()[0] Tx, _, ssq_freqs, *_ = ssq_cwt(x) plot(x, title="linear chirp", show=1) imshow(Tx, abs=1, title="abs(SSQ_CWT)", xlabel="time", ylabel="frequency", yticks=...


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This can be accomplished with an analytic time-frequency representation, like CWT or STFT. Goal must be known precisely to attain desired result, however, as time and frequency are coupled and targeting amplitude alone may yield distortion. The steps are: Transform to time-frequency Zero undesired amplitudes Invert Below I generate linearly amplitude-...


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As I am a newbie in DSP and I thought this article has a clear explanation, I did not try to answer your questions myself. But you said you have read it and thought these questions are still ambiguous, then I want to try one more time to give my answers. First, about the concepts of bins and bands, they confused me a lot in the beginning when I was trying to ...


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At 8kHz sample rate, an 8192 point FFT would give you about 1 Hz resolution. In order to reduce spectral leakage you may want to go larger than this but this will also make it very slow. Depending on your application, it may be a lot easier to just use a time domain bandpass filter. Since your sample rate is way higher than your frequency range of interest ...


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The below tutorial has the clearest explanation I have read about Mel, I think it can answer all of your questions. Mel Frequency Cepstral Coefficient(MFCC) tutorial


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This is a question on fitting an exponential through two points, like That depends on the parent function, which could take on form of: $$ f(x) = ab^x \tag{1} $$ or $$ f(x) = a b_0^x + c \tag{2} $$ where $a, b, c$ are parameters that depend on start and end points, $(x_0, y_0)$ and $(x_1, y_1)$, and $b_0$ is chosen. Answer for 1, for 2, and derivations. I ...


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Since the OP mentions an index of frequency I assume a missing step not shown is an FFT is computed on the M samples, and the algorithm is to determine the maximum frequency. I would not recommend such an approach to determine Doppler offset and fine frequency tuning except for initial acquisition (course tuning), given the computation involved in the FFT ...


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One practical and traditionally used approach when the modulated waveform itself does not need to extend to $f=0$ (as in the case of the OP's wanting the transmit $f+f_\Delta$ is to use a PLL, or even an FLL as depicted in the block diagram below, such that the loop bandwidth of the loop is lower than the desired modulation frequency. The modulation signal ...


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Reconstruction is possible so long as NOLA is obeyed - which is an easier criterion (on synthesis information) to meet than what you seek (analysis information). To discriminate temporal variations finer than $T$, the window's temporal width must be $\leq T$. You can use ssqueezepy's window_resolution with appropriate unit conversion (mult by $f_s$) to ...


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Is there any general thumb rule as to what should be the optimal sampling rate (4x,5x...10x)? This depends a lot on your application, your specific requirements and the typical spectrum of the signals. 9kHz sounds like audio, where something like 2.5x-3x would be a good starting point. A non trivial aspect of sample rate selection is "what can the HW ...


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I work in the field of time and frequency in the design of atomic clocks, and there the notion of the instantaneous frequency for a sum of two tones is very clearly defined and useful. Fat32 touched on this with reference to communications (where I spent most of my career), but it extends far beyond that in more general cases starting with the clear ...


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why does this power measurement (which is an instant function of time) It's NOT a instant function of time. For example instantaneous power of a sine wave is $$ p(t) = x(t)^2 = A \cdot cos^2(t) = \frac{A^2}{2}(1+cos(2t))$$ You have to apply some amount of time averaging to get rid of the $cos(2t)$ component and that's what all spectral analyzer do. : if I ...


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The rotation of the constellation is due to carrier phase offset, which is not the same as a time delay. What the OP is seeing with the additional peaks is evidence that portions of the waveform itself repeat every 0.3x10^6 samples. Since the entire correlation is going down toward the edge of the plot, I assume the OP has done a linear cross-correlation and ...


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This was my first google hit: https://medium.com/analytics-vidhya/understanding-the-mel-spectrogram-fca2afa2ce53 It seems to explain both how and why? Mel frequency binning is afaik only used when human perception is involved. Either directly, or for signals that have probably been adapted to human hearing (such as human speech). It is a way to represent ...


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