The answers to this are now on my site, which I'm not going to keep updating into this answer when I modify it

Ignoring quantisation noise, if you anti alias filter a signal at 2x the nyquist rate and then sample at 2x the nyquist rate then you capture twice the bandwidth of thermal noise. The discrete signal ...

In the end, I worked out that PCM is a function that multiplies a signal with a Dirac comb, rounds them to a quantisation level, and takes the discrete data points as samples and stores them in memory ...

If you decided to represent a time domain sample as an infinitesimal width sinc with main lobe width of $\frac{\pi}{T}$ at a fixed height $A$ centered at $t=0$, instead of a Dirac delta $A\delta(t)$, ...

I feel like the other answers don't state succinctly the step by step process of how the matched filter is used on a concrete example, and what it actually consists of, and why it is needed and how it ...

Companding implies that there is a decompression operation, whereas compression implies that it is lossy compression and the final product, which is just used to compress in a way that cannot be ...

If a piece of music is sampled at 32,000 samples per second (Hz), any frequency components at or above 16,000 Hz (the Nyquist frequency for this sampling rate) will cause aliasing when the music is ...

In the end I came to the conclusion that the maximum spectral efficiency a channel allows with its SNR is $\log_2(1+\frac S N)$. This is a property of an analogue channel with an SNR and is measured ...

Zero stuffing does not insert additional frequencies and the frequencies above the original signal frequency are not present in the original signal; however, because the signal is a set of samples, ...

I think $$R_{xx}(\tau) \triangleq \int_{-\infty}^\infty x(t)x(t+\tau)dt$$ Is just for a continuous signal $X$ that isn't a stochastic process. When it becomes a stochastic process, the expected value ...

This has been resolved. It was due to a misunderstanding of what a pulse filter was. It's used on the ZOH output of the DAC to convolve it, which is a multiplication in the frequency domain, i.e. it's ...

Let's just visualise what we get from the fourier transform of a real signal consisting of real cos frequencies only, in this case $A_c\cos(ct)$, within a centred rect window of length $T$. \$A_{\omega}...