py4DSP

DSP (Digital Signal Processing) code in Python

Intro

• This repo is for my personal study of some DSP (digital signal processing) conceps and to study scipy.signal library
• Jupyter Notebooks have some markdown cells which contain explanations in LaTeX which are sometimes rendered incorrectly by GitHub. So, it is sometimes better to study locally
• Example notebooks start with: /examples/freq_domain/fft_intro.ipynb
• Following examples are linked to the beginning cell of the former notebook
• All code and all examples are prone to all kinds of errors
• Any corrections, suggestions, improvements, etc. are welcome

Contents

• /examples/freq_domain/fft_intro.ipynb
  • Write complex equations in markdown cells
  • FFT math
  • Simulate a sinusoid together with its time vector
  • Take the FFT
  • Plot the signal, plot the FFT, or together
  • Effect of removing the offset from a signal on the FFT
  • Relation between the signal amplitudes and the size of the FFT peaks
• /examples/freq_domain/fft_index_freq_match.ipynb
  • Effect of the size of the FFT
• /examples/freq_domain/spectrogram.ipynb
  • Generate chirp with signal.chirp
  • Different kinds of chirp signals: linear, quadratic, logarithmic, hyperbolic
  • Plot spectrogram together with the signal power
• /examples/lti_filters/filter_bank.ipynb
  • Create a filter object with signal.dlti
  • Design IIR filters with signal.iirdesign
  • Create a filter bank consisting of IIR filters
  • Draw the bode plot
  • Use the filter bank with signal.dlsim which simulates the output of a discrete-time linear system
• /examples/lti_filters/phase_response.ipynb
  • Design FIR filter with signal.firwin
  • Display filter equation in LaTeX
  • Plot filter coefficients
  • Plot impulse and step responses
  • Simulate superposition of sinusoids
  • Given numerator, denumerator, and the input signal, calculate the output of an LTI filter with signal.lfilter
  • Compare similar FIR and IIR filters in terms of phase responses
• /examples/lti_filters/speed.ipynb
  • Use timers to measure execution time
  • Compare similar FIR and IIR filters in terms of speed
• /examples/lti_filters/fir
  • Design low-pass FIR filter
  • Design high-pass FIR filter
  • Design band-pass FIR filter
  • Design band-stop FIR filter
  • Design all-pass FIR filter
  • Design all-stop FIR filter
• /examples/lti_filters/fir/params
  • Number of parameters of an FIR filter is too small
  • Number of parameters of an FIR filter is too big
  • Number of parameters of an FIR filter is even
  • Pass as it is FIR filter
• /examples/lti_filters/iir
  • Design low-pass IIR filter
  • Design high-pass IIR filter
  • Design band-pass IIR filter
  • Design band-stop IIR filter
• /examples/lti_filters/iir/params
  • Bad pass_loss_dB
  • Good pass_loss_dB
  • Good stop_loss_dB
  • All good IIR filter
• /examples/lti_filters/convolution.ipynb
  • Caclulate the impulse response using signal.dimpulse
  • Calculate the LTI filter output using the impulse response and the convolution operation with signal.convolve
  • Compare signal.lfilter with signal.convolve
• /functions/fft.py
  • Functions related to FFT with numpy and matplotlib
• /functions/lti.py
  • Functions related to LTI systems with numpy, matplotlib, and scipy.signal
  • Display LaTeX equations with from IPython.display import Latex, display

To Do List

• Study and demonstrate wavelet basics. Find a popular and stable library if any exists. Implement yourself otherwise
• Study and demonstrate wavelet scattering basics
• Linear algebra review. Study a popular and stable library

My Other Study Repos

• py4ML: ML code in Python
• py4Nav: Navigation code in Python
• py4Me: Daily code in Python

Written by serhatsoyer