Digital Signal Processing

notes.md

Think DSP

1. Discrete Fourier Transofrm
2. Convolution Theorem
3. Linear Time-Invariant Theory

Signal: It represents a continuous mathematical function

Wave: Contains an array of discrete samples

Spectrum: Contains the DFT of a Wave

Signal ------> Wave <-----> Spectrum

Spectral Analysis

• Any signal can be represented as a sum of single frequency components
• The Spectrum of a signal encodes the amplitude of each component

Discrete Fourier Transform (DFT)

• DFT of a wave is its soectrum
• FFT is an efficient algorithm

def make_spectrum(ys, framerate):
  hs = np.fft.rfft(ys)
  n = len(ys)   # no. of samples
  d = 1/framerate # time between samples
  fs = np.fft.rfftfreq(n,d)
  
  return Spectrum(hs,fs, framerate)

Filtering

• A filter modifies a signal by amplifying.attenuating some components more than others
• Low-pass filter: Attenuates high frequencies, lets low frequencies pass

Aliasing

• We lose information on when we sample
• If the sample rate is 10000 Hz the highest we can sample is 5000 Hz