Analytic signal, Hilbert transform, and FFT — envelope and instantaneous phase
How the analytic signal and Hilbert transform give envelope and instantaneous phase/frequency, FFT implementation tips, and links to the envelope follow-on.
Sampling Theorem
Sampling in Matlab and downsampling an audio file
Generating a continuous signal and sampling it at a given rate is demonstrated here. In simulations, we may require to generate a continuous time signal and convert it to discrete domain by appropriate sampling. For baseband signal, the sampling is straight forward. By Nyquist Shannon sampling theorem, for faithful reproduction of a continuous signal in … Read more
Sampling Theorem – Bandpass or Intermediate or Under Sampling
Prerequisite: Sampling theorem – baseband sampling Intermediate Sampling or Under-Sampling A signal is a bandpass signal if we can fit all its frequency content inside a bandwidth $latex F_b $. Bandwidth is simply the difference between the lowest and the highest frequency present in the signal. “In order for a faithful reproduction and reconstruction of … Read more
Sampling theorem (Nyquist) — baseband sampling without aliasing
Nyquist–Shannon sampling for baseband signals: sample faster than twice the highest frequency, or aliases fold into band.