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

Remote measurement of physiological signals from videos is an emerging topic.  Currently, I adapt part of our work in the FaceHeart  and CSSP to participate in the CVPM2020 Challenge. (belonging to IEEE CVPR).  And we obtain the third position from a total of 125 participants / 25 submits worldwide. Detail URL:  https://competitions.codalab.org/competitions/22287#learn_the_details My Google Scholar:  https://scholar.google.com.tw/citations?user=sklHe5cAAAAJ&hl=zh-TW&oi=sra

For me, one better description of the  general linear phase (GLP)  is a  constant group delay . By definition, group delay is a negative derivative of phase [1] (In fact, the detailed phase/delay relationship can be derived but I suggest we just accept them.). Then, the Derivative (group delay) of a linear (phase) is constant and vise versa. Then, let's move on to the meaning of group delay. the group delay of a frequency represents the delay unit of the filter to that frequency. So, the filter may treat different frequencies with different delay units. For an extremely bad example of a non-linear filter, the input signal 'do re mi' may becomes 're mi do' in the output. A GLP filter can guarantee that such weird condition will never happen. Github link ----------------------------------------------------------------------------------- Here I wrote an example. The example comes from Chapter 5.1.2 in the bible of DSP[2] and I just implemented the sample. Fi

Reconstruction is essentially a kind of interpolation or so-called digital to analog conversion (DAC). Detail descriptions are introduced in chapter 4.8.3 of the DSP Bible [1]. Although we all understand the basic sampling theory, the problem is how to bridge the theory and practice . Because all the signals we can simulate in Matlab are essential 'Digital'. So, the so-cal ADC/DAC is just an approaching simulation. Let me briefly justify the difference. Ideal Reconstruction in DAC:  There is typically a zero order hold circuit and reconstruction filter. Please note that the frequency response of zero-order hold is not evenly flat so a reconstruction filter comes into an aid. Matlab Simulation in DAC: There is no need to actually simulate a zero-order hold. All you need are an upsampling and an ideal low pass filter. This sample code sample a simulated 2 Hz analog signal,x_a, (with sampling rate 1500 Hz) to a discrete-time signal,x_d, with 5 Hz sampling rate (near

    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