Digital Filter design and Analysis with Python

This Project contains mainly two parts, which are filter design and utiliy usage when understanding and implementing filter.

Filter Filter design and analysis

What is a filter in the signal? Filter can be used to remove unwanted noise or unwanted signal, to modify the signal, to imitate new signal, or analyze the meaning in the signal such as brain wave. In this part, we will design this filter using several methods and this is specifically for the signal from wav file while using music, recording, and streaming phone call.

Filter can be basically designed as fir and iir as single filter. In this case it has several options to design the filter. such as Q factor, Bandwidth, Amplitude, Phase, etc. (If you want to know more about it, please check the link^1). This project is for plotting the transfer function and processing the signal from wav file while using several filter.

This part is written in main.py, and the contents is as below,

Single filter design

A filter has several forms, which are lowpass, highpass, bandpass, allpass notch, peaking, and shelf. In this case, it will design using biquied form transfer function. The filter_plot can be used to plot these kinds of filter, and show the frequency response, phase response, and poles and zeros. The filter process can show how to process the signal in wav file, and make the wav file specific path. (If you want to know more about it, please check the path, it referred following link)^2
```
 - filter_plot
 - filter_process
```
Serial structure of filters design

Serial structure of filters, which is also called Parametric Equalizer in the music field. "Parametric" means it will use biquid(especially two zeros and two poles) form transfer function. This follows the steps like single filter design, which are plot and process.
```
 - serial_equalizer_plot
 - serial_equalizer_process
```
Parallel structure of filters design

Parallel structure of filters, which is also called Graphical Equalizer in the music field. It designed this combination of filters using least square method in the real impulse response and also include the complex impulse response(but it commented in the part of computation). This follows the steps like single filter design, which are plot and process. Before understanding, it provides the test vector using generator_test_vector_grahpical_equalizer function. This part is based on Paper. "Efficient Multi-Band Digital Audio Graphic Equalizer with Accurate Frequency Response Control"
- generator_test_vector_grahpical_equalizer
- parallel_equalizer_plot
- parallel_equalizer_wav_process
Analyze filter

This part integarate single, serialm and parallel filters design. It will plot the transfer function, phase response, and poles and zeros for analying each of the filters.
- analyze_filter

Utility for understanding and implementing filter

The contents is as below,

Fi command example between fixed and floating format parameter test

When computing several filters in restricted enviroment such as embedded device, it need to consider the format of the parameter. This part provides the example of fixed format and converting between floating and fixed format using fi command imitating Matlab fi command.
- example_fi
- iir_filter_fixed_to_floating_format_plot
- iir_filter_float_ng_to fixed_format_print
- iir_filter_fixed_to_floating_format_process
Logarithmic scale

This part is used to plot the logarithmic scale of the frequency response.
- scale_logarithmic
Analying the difference between digital and analog

This part is used to understand how to plot digital and analog filter, and connect to know the difference between digital and analog filter.
- paper_plot_sheving_filter_digital
- paper_plot_sheving_filter_analog
Frequency wrapping

This part contains the frequency wrapping referring to frequency-warped signal preprocessing for audio application, 2000.
- paper_all_pass_filter

Result

This part contains the simulation result of the filter design and analysis, and the result of wav file. When analyzing the result, it used Audacity to make a frequency response. It tested the each type of filer with white noise since representing expected frequency response well. The original frequency response in Audacity's frequency response is as below,

I designed single filter such as peaking and shelving form, serial structure of 3 peaking filters and parallel structure of filters which frequency is located with logarithmic scale. The results constitute filter parameter, expected frequency response and wav file response. The wav file can be seen in this path. You can also make the this result using main.py. I attached the results as below,

Single filter design

Peaking filter
1. Filter parameter
```
 Q = 1/sqrt{2}
 gain = 6 (dB)
 fc = 1033 (Hz)
```
  *fc = cut-off frequency
2. Frequency response in simulation
3. Frequency response in Audacity
Shelving filter
1. Filter parameter
```
 Q = 1/sqrt{2}
 gain = 6 (dB)
 fc = 1033 (Hz)
```
2. Frequency response in simulation
3. Frequency response in Audacity

Serial structure of filters design

Three peaking filters
1. Filter parameter
```
 Q = 4
 gain = 12 (dB)
 fc = 1000, 4000, 8000 (Hz)
```
2. Frequency response in simulation
3. Frequency response in Audacity

Parallel structure of filters design

32 band
1. Filter parameter
  
  Test case 1, test_gain 2, ["1"]["test_gain"][1]
2. Frequency response in simulation
3. Frequency response in Audacity
64 band
1. Filter parameter
  
  Test case 2, test_gain 2, ["2"]["test_gain"][1]
2. Frequency response in simulation
3. Frequency response in Audacity

Reference

Rämö, Jussi, Vesa Välimäki, and Balázs Bank. "High-precision parallel graphic equalizer." IEEE/ACM Transactions on Audio, Speech, and Language Processing 22.12 (2014): 1894-1904.

Citation

If any question, ask or contact to me!

@article{,
  title={Digital Filter Design for Audio and Speech Processing},
  author={Seunghyun Oh},
  year={2022}
}

ooshyun / Digital-Filter-Design