4 votes
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Unwanted periodicity in data

Some time-frequency analysis with the synchrosqueezed CWT, where I guess fs=10000 but this doesn't matter except for axis labels and physical interpretation. 1. ...
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4 votes

Time-varying Notch Filter in C

A few ideas: If you are implementing this as an IIR filter, use Direct Form I. This minimizes the discontinuity of the state variables (which are simply input and output). A biquad notch filter can be ...
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4 votes
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Bilinear transform for a system in zero-pole-gain form

OK, from this answer we know it should be normalized at DC, i.e., let $s=0$ and $z=1$ $$ k_a \frac{\prod_{n=1}^N{(s-z_{a, n})}}{\prod_{n=1}^N{(s-p_{a, n})}}\Bigg|_{s=0} = k_d \frac{\prod_{n=1}^N(z-z_{...
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4 votes
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What is the relationship among digital filter cutoff frequency, signal frequency and filter settling time?

With "Settling Time" we can consider the overall time delay of the filter, and the rise/fall time of a transient change going through the filter. The rise/fall time will inversely related to ...
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3 votes

What is the relationship among digital filter cutoff frequency, signal frequency and filter settling time?

(1) Filter settles slower if the ratio between signal frequency and filter cutoff frequency is smaller; (2) Filter settles slower if bandwidth of a band-pass filter is narrower: Correct in the sense ...
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3 votes
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how to design the $\text{sinc}(\cdot)$ filter for OFDM oversampled system

Resampling the transmit OFDM waveform in the frequency domain by zero-padding the FFT prior to taking the IFFT has the advantage of simplicity and maintaining sub-carrier orthogonality (no inter-...
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2 votes
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Sampling frequency in bilinear transform when designing butterworth filter

Bilinear transform has a nonlinear frequency mapping $$ \varOmega = \frac{2}{T}\tan{\frac{\omega}{2}} $$ Substituting $\varOmega = 1$ and $\omega = 0.5\pi$ into it and you can derive that $$ T = 2 $$ ...
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1 vote

Bilinear transform for a system in zero-pole-gain form

Since z and p are already calculated, it follows that the result of the prod() is a number. ...
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1 vote

What is the relationship among digital filter cutoff frequency, signal frequency and filter settling time?

If the filter is 2nd order then the exponential decay governing the impulse response will be given by: $$\text{e}^{\ln(|p|)n} \tag{1b}\label{1b}$$ (see this answer for a more detailed explanation) $p$ ...
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How to design digital Butterworth filter and return its zeros, poles and gain

This can be designed in the following steps: Design a $N$-th order lowpass prototype of the analog Butterworth filter and you get an all-pole filter with poles $$ p_{a, n} = e^{j\pi(2n-1+N)/2N}, \ \ \...
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