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0

You can solve this with high-school algebra and the time delay property $$ \mathcal{Z}(x(n-k)) = z^{-k} X(z) $$ Applying this to your expression $$y(n)=2x(n)-1x(n-1)+3x(n-2)$$ we get $$Y(z) = 2 X(z) - X(z)z^{-1} + 3X(z)z^{-2}$$ $$\frac{Y(z)}{X(x)} = 2z^{-2} - z^{-1} + 3$$ The denominator is null because the filter is not recursive


4

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 ...


1

If it's not obvious from the other three (at this writing) answers: scale it to match he problem at hand. All of the three suggested scalings so far (energy = 1, DC gain = 1, maximum coefficient = full scale for your data type, then scale the output) are valid in different circumstances. And don't sweat over trying to find a universal "correct" ...


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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 ...


1

I recommand to have the input and the output of the filter at same level (resampling included). This means a gain of 1 in linear or 0 dB. It is consistant and useful for reuse. The best way to preliminary verify for the gain on a low pass filter is to inject a DC constant signal. Usualy, I tune the taps level to compensate the fractional part of the gain. ...


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My recommendation is to normalize the filter impulse response to have energy equal to 1. In continuous time, the digital communication system will transmit a symbol $a_i$ using the pulse $$s(t) = a_ip(t),$$ where $p(t)$ is an RRC pulse. The receiver will recover $a_i$ from $s(t)$ using a matched filter: \begin{align} a_i &= \int_{-\infty}^\infty a_i p(t)...


1

I wanted to ask what are the techniques which can be used to extract this sub-band data? That's a description of a filter bank. Yes, the FFT can be used for such applications. You'll find that OFDM, which powers DVB-T, 4G/5G, WiFi, … (basically all high-speed wireless terrestrial links) does exactly that. You'll also find that if you find the inherent sinc-...


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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 ...


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