6

If a first-order IIR will do, modify that slightly, and you're done. So the usual first-order low-pass filter can be defined as $y_n = h(\theta_n)$ such that $y_n = y_{n-1} + a(\theta_n - y_{n-1})$. This works great for $\theta_n \in \mathbb{R}$. You want a low-pass filter that's defined on an interval that spans $360^\circ$. For reasons that will become ...


6

Minimum phase filters will not give you a near constant group delay. You can design a non-linear phase FIR filter with a linear desired passband phase with a specified group delay that is smaller than the group delay of the corresponding linear phase filter. If you use a least-squares criterion, this is equivalent to solving a system of linear equations. As ...


6

In principle there is no reason why the filter order of a general bandpass or bandstop filter must be even. Such a restriction is a consequence of a specific design procedure. In classic IIR filter design (Butterworth, Chebyshev, Cauer) you start with an analog prototype lowpass filter. Bandpass or bandstop filters are then obtained by a frequency ...


5

In a PDM microphone, the sigma-delta convertor pushes the noise to frequency regions above the 0-20kHz spectrum. So if you'd take the FFT of the signal that comes directly from the PDM microphone, the straight zeros and ones, and only look at the bins that fall in the 0-20kHz region, you'd get the data that you need. You can see this here, where a 16kHz sine ...


5

What you are looking for are what we, in the audio space, call comb filters. Comb filters may or may not have a feedback path, just like FIR and IIR filters. In fact, there is a generalized theory about designing comb filters based simply on designing any digital filter. In fact, you can think of every LTI digital filter as being a comb filter where the ...


4

Hopefully you'll get a bunch of answers here from the very general to the super specific. I'll put in my two cents here. The recommendations I would make are from the field of radar and communication systems. These systems tend to exercise almost all aspects of signal processing: Signal generation and mixing Sampling, decimating/upsampling Signal ...


4

Median filtering is non-linear, and pretty awesome about removing outliers. You just need to adjust the length of the filter based on the estimate of the frequency of the errored samples.


4

This is three years later, but since I don't see the real answer posted here, I will post it. The correct answer is that if we are literally interpreting the original statement as a purely mathematical claim, taken at face value, then it is incorrect. There do exist causal filters, even minimum-phase ones with nice closed-form Fourier domain expressions, ...


4

The purpose of pulse shaping filters is not to overcome ISI as is implied in the OP's question. The only reason for using a pulse shaping filter is spectral efficiency, and in the process ISI can be introduced if not done properly. In order to limit bandwidth, pulse shaping must extend the time domain response for each pulse beyond a symbol boundary, but can ...


4

If the OP is actually interested in selecting only one individual frequency from the even or odd harmonics, then a moving average filter (MAF) would be ideal since this can provide a null at every other frequency when the frequencies are harmonically related. The low-pass MAF with all the coefficients as 1 will pass DC at $f=0$ and provide nulls spaced by $1/...


3

The A/D can be placed as a single real A/D before the multipliers, OR as shown in the diagram as two A/Ds one after each multiplier to sample the I and Q channels. In either case, an analog filter is required before any A/D conversion as an anti-alias filter. This can be a bandpass filter or a low-pass filter, depending on which image in the analog domain's ...


3

A good way to deal with circular (directional) averages is to turn it into a vector average. To find the average angle $\bar{\theta}$ of several angles $\theta_n$ (in radians) then: $$ \bar{\theta} = \arg \left ( \sum_{n=0}^{N-1} e^{i \theta_n} \right ) $$ where $\arg$ is the argument (angle) of the resulting complex sum. There's some more stuff about this ...


3

As you can see, the second measurement of 358 is an erroneous measurement. Why would that be erroneous? Phase is periodic with $2\pi$ or 360 degrees. That means 358 degrees is the same angle as -2 degrees. Your data looks perfectly fine if you look at it as 2, -2, 3, 5, 10, 18 , ... What you probably need is phase "unwrapping". If you see a ...


3

I believe your thinking is correct. For bandpass filters, for each z-plane pole in the positive-frequency range there's a conjugate pole in the z-plane's negative-frequency range. So for bandpass filters there will all be an even number of total z-plane poles (two poles, four poles, six poles, etc.). When using MATLAB's ellipord command for bandpass filters ...


3

Maybe that's a just a matter of semantics. You can certainly cascade an even order high pass with an odd order lowpass and you get something that's an odd order filter that sure looks like a bandpass. %% odd order bandpass fs = 44100; fc = 1000; [z,p,k] = butter(2,fc/sqrt(2)/fs*2,'high'); sos = zp2sos(z,p,k); [z,p,k] = butter(3,fc*sqrt(2)/fs*2); sos = [sos; ...


3

You can use kurtosis as a measure of how 'peaky' your signal is. Or the flatness measure, which is the ratio of the geometric mean of the signal to its arithmetic mean. Any signal which is not relatively flat will have a flatness value near 0. $$\text{Flatness} = \frac{\sqrt[N]{\prod_{n=0}^{N-1} x(n)}}{\frac{1}{N} \sum_{n=0}^{N-1} x(n)}$$


3

but what does the stability mean when talking about a system? It means that all poles are INSIDE the unit circle. and if so how does it turn out that when a system is causal and stable its also min phase. Sorry, you got this wrong. Causal, stable and LTI does NOT imply minimum phase. A simple counter examples is a one-sample delay. It's causal, stable and ...


3

Yes, of course. Any delay will look like this where the size of the delay determines the slope of the phase. If the the delay turns out to be an integer number of samples, than this very easy to implement. You can also do fractional delays but that's more work and can only be done approximately.


3

The z-transform is the discrete version of the Laplace transform and in both cases z and s are the set of all complex numbers, and as such we map with the transform the time domain function into the domain of complex frequencies; signals that change in rotation only which is the Fourier Transform and in addition to that such signals that can grow and decay ...


3

Well, if I were doing this from scratch, I would do this with biquad notch filters with very high Q and adjustable coefficients. Two or three of them with frequencies that are harmonically locked. An algorithm could be measuring the difference between the notches and a "wire" and very slowly adjust the fundamental frequency and maximize that ...


3

As long as you make the target conjugate symmetric the inverse FFT will be real (with maybe some residual numerical noise that you can simply zero out) If you want to use a least square error fit, just split the equations into their real and imaginary parts. I.e. instead having $N$ complex equations, you will have $2N$ real equations. Sharp phase transients ...


3

Observe the magnitude of frequency response (rescaled to 0 to 1): where $$ \begin{align} H(\omega) &= e^{-j 0\omega} - e^{-j 1\omega} + e^{-j 2\omega} \\ &= 1 - e^{-j 1\omega} + e^{-j 2\omega} \tag{1} \end{align} $$ following the time-shift property: $$ x(t - t_0) \Leftrightarrow e^{-j t_0 \omega} X(\omega) \tag{2} $$ Though it isn't particularly ...


2

The canonical way to remove an echo (it can be either electrical echo, or acoustic echo) from a signal is by using adaptive filters. Such an adaptive filter should be able to hold a model of an echo path in the form of an impulse response of this path. Having this model, we can use an original signal to create a copy of its echo, so it can be then subtracted ...


2

The book: Richard G. Lyons (Editor), Streamlining Digital Signal Processing: A Tricks of the Trade Guidebook 2nd Edition, Wiley-IEEE Press; 2nd edition (July 2, 2012) is a compendium of short application-specific signal processing algorithms. Disclaimer: I wrote one of the chapters with Eric Jacobsen, but I do not benefit monetarily from the sales of the ...


2

First of all, the correct equation for an RRC pulse is given here. You are correct that you need to define the sampling frequency Fs and the symbol interval Ts. The number of samples per symbol interval is then Ts*Fs, which I assume to be an integer. You also need to define beta, and the pulse duration D. For simplicity, let's assume D is given as a multiple ...


2

Why do I have ringing and such an aggressive response? Because you designed a really aggressive filter, which is borderline unstable. All the poles are less than 1/1000 away from the unit circle. How does the low cut off frequency and high sample rate affect the filter response? The lower the cutoff, the higher the order, and the higher the sample rate, ...


2

The gain is completely arbitrary and you can scale it as desired for the overall receiver or transmitter design. Where special attention must be paid is with fixed point design where the best practice is to let the filters grow the signal- do not scale the coefficients or the input as that only introduces more quantization noise and degrades SNR. Let the ...


2

GMSK doesn't just use a Gaussian filter instead of a raised-cosine filter. It uses a Gaussian filter on the phase, before applying it to the modulator. This makes it a nonlinear operation. When a raised-cosine filter is applied to some modulated signal, it is applied after modulation, as a linear operation. So there's a whole lot of convenient rules about ...


2

(Assuming the context is FSK signals, where the pulse shape is applied to the phase, instead of the amplitude as in linear modulation). The main reason is that the sideband and out-of-band emissions of GMSK are lower than those produced with a raised cosine filter. See for example this plot from Wikipedia: https://en.wikipedia.org/wiki/File:GMSK_PSD.png This ...


2

The modifier normal is meant to distinguish the form from the transposed form. So there is a normal direct form I, a transposed direct form I, and similarly for the direct form II. As far as I know, this terminology is not universal, and I've only come across it in books (co-)written by Manolakis or Ingle.


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