Sketches of Digital Signal Processing, Remote Photoplethysmography, and Image Signal Processor

    When it comes to estimating the main frequency of sinusoidal like signals with finite length , the most intuitive method might be observing the largest component in the DFT/DTFT. Nonetheless, the resolution of DFT is limited by windowing effect. If a known structure of the signals is given, these method are not the best way to estimate the frequency.     With the known structure of the signals, Professor Oppenheim introduced an alternative way to estimate frequency, Parametric Signal Modeling (a.k.a. Autoregressive model, AR Model) [1] . To apply this method, a structure of all-pole linear system , H(z), should be predefined. This all-pole system tries to represent the signal with relative small set of parameters (or coefficients). Then, we estimate the coefficients of the system with observed signals. Last, the DTFT of the system can be regarded as the power spectrum density (PSD) of the observed signals.     There are two basic methods to estimate coefficients from a obs

The complexity of DFT/IDFT using FFT/IFFT is only n*log2n whereas the complexity of convolution is n square. Then, why do we need to learn so many methods to design a filter? Why is it a bad idea to filter by zeroing out FFT bins? This question might be the most confusing one when learning DSP. To verify this fact is simple, we just need to  cautiously  observe the spectrum of the impulse response of an ideal(?) bandpass filter which just zeros out FFT bins. Why do I need to add the adverb "cautiously"?  If we just use the same size of the FFT to observe the response of the impulse, we will be deceived as shown in Fig 1. Nonetheless, if we add the order of DFT when observing the output of the filter, that is, zero-padding the impulse response, we can find the so-called Gibbs phenomenon, ripples in the frequency domain, as depicted in Fig.2. The results in fact come from the windowing effect. If you want to entirely understand the problem, please refer to chapter 7.6