Sci py india_conference_2019
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1. The document discusses digital signal processing concepts and exercises using Python packages like NumPy, SciPy and Matplotlib. 2. It provides instructions on installing the required software packages for Windows, Ubuntu Linux and Android systems. 3. A list of 20 exercises is given covering topics like continuous and discrete sine waves, convolution, DFT using fft and own function, windowing techniques and design of FIR and IIR filters.
![References:
[1]. https://spoken-tutorial.org/cdcontent/
[2]. https://python.fossee.in/self_learningcourse/
https://python.fossee.in/spoken-tutorials/
[3]. https://matplotlib.org/3.1.1/gallery/lines_bars_and_markers/stem_plot.html#sphx-glr-
gallery-lines-bars-and-markers-stem-plot-py
[4]. https://matplotlib.org/devdocs/gallery/subplots_axes_and_figures/subplots_demo.html
[5]. https://docs.scipy.org/doc/numpy/reference/generated/numpy.convolve.html
[6]. https://docs.scipy.org/doc/numpy/reference/generated/numpy.zeros.html
[7]. https://scipy-cookbook.readthedocs.io/items/FIRFilter.html](https://image.slidesharecdn.com/scipyindiaconference2019-200802184547/85/Sci-py-india_conference_2019-8-320.jpg)
![References:
[9]. http://mpastell.com/pweave/_downloads/FIR_design_rst.html
[10]. http://mpastell.com/pweave/_downloads/FIR_design_rst.html
[11]. http://mpastell.com/2009/05/11/iir-filter-design-with-python-and-scipy/](https://image.slidesharecdn.com/scipyindiaconference2019-200802184547/85/Sci-py-india_conference_2019-9-320.jpg)
![1. Generation of Sine Waveform
[refer 1_Continuous_sine_wave.py]
𝑥 𝑡 = 𝐴 ∗ 𝑠𝑖𝑛 2 ∗ 𝜋 ∗ 𝑓 ∗ 𝑡](https://image.slidesharecdn.com/scipyindiaconference2019-200802184547/85/Sci-py-india_conference_2019-13-320.jpg)
![2. Generation of Discrete & Continuous Sine Waveform [refer
2_cont_Discrete_sinewave.py]](https://image.slidesharecdn.com/scipyindiaconference2019-200802184547/85/Sci-py-india_conference_2019-14-320.jpg)
![3. Amplitude change in Sine waveform [refer Exercise no.3]](https://image.slidesharecdn.com/scipyindiaconference2019-200802184547/85/Sci-py-india_conference_2019-15-320.jpg)
![4. Stem plot Sine waveform [refer Exercise no.4]](https://image.slidesharecdn.com/scipyindiaconference2019-200802184547/85/Sci-py-india_conference_2019-16-320.jpg)
![5. Linear Convolution [refer Exercise no.5]
N = Length of Linear convolution result
N1 = Length of x[n]
N2 = Length of h[n]
N = N1+N2-1
𝑦 𝑛
= 𝑥 𝑛 ∗ ℎ 𝑛𝑦 𝑛
=
𝑘=0
𝑁−1
𝑥 𝑘 ℎ 𝑛 − 𝑘](https://image.slidesharecdn.com/scipyindiaconference2019-200802184547/85/Sci-py-india_conference_2019-17-320.jpg)
![6. Auto correlation [refer Exercise no.6]
N = Length of Auto correlation result
N1 = Length of x[n]
N2 = Length of x[-n]
N = N1+N2-1
𝑦 𝑛
= 𝑥 𝑛 ∗ 𝑥 −𝑛](https://image.slidesharecdn.com/scipyindiaconference2019-200802184547/85/Sci-py-india_conference_2019-18-320.jpg)
![7. Cross correlation [refer Exercise no.7]
N = Length of Cross correlation result
N1 = Length of x[n]
N2 = Length of h[-n]
N = N1+N2-1
𝑦 𝑛
= 𝑥 𝑛 ∗ ℎ −𝑛](https://image.slidesharecdn.com/scipyindiaconference2019-200802184547/85/Sci-py-india_conference_2019-19-320.jpg)
![8. Discrete Fourier Transform using fft
library package[refer Exercise no.8]
Let x[n] is a discrete sequence, the N-point of Discrete Fourier Transform of x[n] is given
by,
Inverse Discrete Fourier Transform is given by,
𝑋 𝐾
=
𝑛=0
𝑛=𝑁−1
𝑥 𝑛 𝑒
−𝑗∗2∗𝜋∗𝐾∗𝑛
𝑁
𝑥 𝑛
=
1
𝑁
𝐾=0
𝐾=𝑁−1
𝑋 𝐾 𝑒
𝑗∗2∗𝜋∗𝐾∗𝑛
𝑁](https://image.slidesharecdn.com/scipyindiaconference2019-200802184547/85/Sci-py-india_conference_2019-20-320.jpg)
![9. DFT – Magnitude and Phase Spectrum
[refer Exercise no.9]
Let x[n] is a discrete sequence, the N-point of Discrete Fourier Transform of x[n] is given by,
Magnitude spectrum = |X(K)|
Phase spectrum = tan-1(Image part (X(K))/Real Part(X(K))
𝑋 𝐾
=
𝑛=0
𝑛=𝑁−1
𝑥 𝑛 𝑒
−𝑗∗2∗𝜋∗𝐾∗𝑛
𝑁](https://image.slidesharecdn.com/scipyindiaconference2019-200802184547/85/Sci-py-india_conference_2019-21-320.jpg)
![10. DFT – using own formula based
function [refer Exercise no.10]
* Use cmath Library for complex number
Manipulations
* Initialize X(K) with complex zeros ‘0+0j’
* Initialize X(K) with numpy zeros cause float type
assign to complex type error
* This problem will not occur in fft() built-in
function](https://image.slidesharecdn.com/scipyindiaconference2019-200802184547/85/Sci-py-india_conference_2019-23-320.jpg)
![11. Power Spectrum Estimation [refer
Exercise no.11]
𝑃𝑥𝑥 𝐾
=
1
𝑁
𝑋 𝐾 2
𝑋 𝐾
=
𝑛=0
𝑛=𝑁−1
𝑥 𝑛 𝑒
−𝑗∗2∗𝜋∗𝐾∗𝑛
𝑁
The power spectrum of a discrete sequence x[n] is given by,
Where X(K) is the
Discrete Fourier
Transform of x[n]](https://image.slidesharecdn.com/scipyindiaconference2019-200802184547/85/Sci-py-india_conference_2019-24-320.jpg)
![12. Windowing techniques used for FIR
Filter Design [refer Exercise no.12]
*Rectangular window
*Hamming Window
*Hanning Window
*Blackmann Window
*Bartlett window](https://image.slidesharecdn.com/scipyindiaconference2019-200802184547/85/Sci-py-india_conference_2019-26-320.jpg)
![13. FIR- Low Pass Filter-Windowing
technique [refer Exercise no.13]
h[n] = hd [n]*W[n]
hd [n] = FIR LPF impulse response
W[n] = Hamming window function
hd [n] = sin(wc*(n-(N-1)/2)) / (π*(n-(N-1)/2))](https://image.slidesharecdn.com/scipyindiaconference2019-200802184547/85/Sci-py-india_conference_2019-27-320.jpg)
Sci py india_conference_2019
- 1. Digital Signal Processing using Python Dr.R.Senthilkumar, Assistant Professor, Department of Electronics and Communication Engineering, Institute of Road and Transport Technology, Erode, Tamilnadu SciPy India Conference 2019 Venue: IIT Bombay Date: 29 th Novemeber 2019
- 2. Software Packages to be Installed For Windows and Ubuntu Linux Users ● Matplotlib ● NumPy ● SciPy ● Pylab
- 3. Windows Users Download the software Python3.7 from python.org ● Install the packages: Matplotlib, Pylab, SciPy, NumPy using pip command ● Open the software installed directory, Example ● D:python37 ● Using pip command as ● D:python37pip install matplotlib
- 4. Ubuntu Linux Users Better Install Python3.7 using Synaptic Packet Manager ● Since Ubuntu Linux has Python2.7 by default ● Don’t prefer pip command ● The packages NumPy, SciPy will be installed in Python2.7 not Python3.7 ● From terminal invoke Python3.7 as, ● $ Python3 program1.py
- 5. Android Mobile Phone Users Install Pydroid3 using google play store ● Install the packages except Pylab using pip command similar to windows ● Run the programs either in terminal or Run icon ● Disadvantage- only one figure window open at a time ● Other usages similar to windows and Linux
- 6. 1. Continuous Sine Waveform 2. Discrete Sine Waveform 3. Sine waveform Amplitude change 4. Stem plot of Sine Waveform 5. Linear convolution 6. Auto correlation 7. Cross correlation 8. Discrete Fourier Transform Using fft library in SciPy 9. Magnitude and Phase Spectrum plot 10. Discrete Fourier Transform using Formula(own function) 11. Power Spectrum Estimation 12. Window functions used for FIR Filter Design 13. Low Pass FIR Filter window Based and Digital Filter List of Exercises
- 7. List of Exercises 14. High Pass FIR Filter window Based and Digital Filter 15. Band Pass FIR Filter window Based and Digital Filter 16. Band Stop FIR Filter window Based and Digital Filter 17. Low Pass IIR Butterworth Filter Analog and Digital Filter 18. High Pass IIR Butterworth Filter Analog and Digital Filter 19. Band Pass IIR Butterworth Filter Analog and Digital Filter 20. Band Stop IIR Butterworth Filter Analog and Digital Filter
- 8. References: [1]. https://spoken-tutorial.org/cdcontent/ [2]. https://python.fossee.in/self_learningcourse/ https://python.fossee.in/spoken-tutorials/ [3]. https://matplotlib.org/3.1.1/gallery/lines_bars_and_markers/stem_plot.html#sphx-glr- gallery-lines-bars-and-markers-stem-plot-py [4]. https://matplotlib.org/devdocs/gallery/subplots_axes_and_figures/subplots_demo.html [5]. https://docs.scipy.org/doc/numpy/reference/generated/numpy.convolve.html [6]. https://docs.scipy.org/doc/numpy/reference/generated/numpy.zeros.html [7]. https://scipy-cookbook.readthedocs.io/items/FIRFilter.html
- 9. References: [9]. http://mpastell.com/pweave/_downloads/FIR_design_rst.html [10]. http://mpastell.com/pweave/_downloads/FIR_design_rst.html [11]. http://mpastell.com/2009/05/11/iir-filter-design-with-python-and-scipy/
- 13. 1. Generation of Sine Waveform [refer 1_Continuous_sine_wave.py] 𝑥 𝑡 = 𝐴 ∗ 𝑠𝑖𝑛 2 ∗ 𝜋 ∗ 𝑓 ∗ 𝑡
- 14. 2. Generation of Discrete & Continuous Sine Waveform [refer 2_cont_Discrete_sinewave.py]
- 15. 3. Amplitude change in Sine waveform [refer Exercise no.3]
- 16. 4. Stem plot Sine waveform [refer Exercise no.4]
- 17. 5. Linear Convolution [refer Exercise no.5] N = Length of Linear convolution result N1 = Length of x[n] N2 = Length of h[n] N = N1+N2-1 𝑦 𝑛 = 𝑥 𝑛 ∗ ℎ 𝑛𝑦 𝑛 = 𝑘=0 𝑁−1 𝑥 𝑘 ℎ 𝑛 − 𝑘
- 18. 6. Auto correlation [refer Exercise no.6] N = Length of Auto correlation result N1 = Length of x[n] N2 = Length of x[-n] N = N1+N2-1 𝑦 𝑛 = 𝑥 𝑛 ∗ 𝑥 −𝑛
- 19. 7. Cross correlation [refer Exercise no.7] N = Length of Cross correlation result N1 = Length of x[n] N2 = Length of h[-n] N = N1+N2-1 𝑦 𝑛 = 𝑥 𝑛 ∗ ℎ −𝑛
- 20. 8. Discrete Fourier Transform using fft library package[refer Exercise no.8] Let x[n] is a discrete sequence, the N-point of Discrete Fourier Transform of x[n] is given by, Inverse Discrete Fourier Transform is given by, 𝑋 𝐾 = 𝑛=0 𝑛=𝑁−1 𝑥 𝑛 𝑒 −𝑗∗2∗𝜋∗𝐾∗𝑛 𝑁 𝑥 𝑛 = 1 𝑁 𝐾=0 𝐾=𝑁−1 𝑋 𝐾 𝑒 𝑗∗2∗𝜋∗𝐾∗𝑛 𝑁
- 21. 9. DFT – Magnitude and Phase Spectrum [refer Exercise no.9] Let x[n] is a discrete sequence, the N-point of Discrete Fourier Transform of x[n] is given by, Magnitude spectrum = |X(K)| Phase spectrum = tan-1(Image part (X(K))/Real Part(X(K)) 𝑋 𝐾 = 𝑛=0 𝑛=𝑁−1 𝑥 𝑛 𝑒 −𝑗∗2∗𝜋∗𝐾∗𝑛 𝑁
- 23. 10. DFT – using own formula based function [refer Exercise no.10] * Use cmath Library for complex number Manipulations * Initialize X(K) with complex zeros ‘0+0j’ * Initialize X(K) with numpy zeros cause float type assign to complex type error * This problem will not occur in fft() built-in function
- 24. 11. Power Spectrum Estimation [refer Exercise no.11] 𝑃𝑥𝑥 𝐾 = 1 𝑁 𝑋 𝐾 2 𝑋 𝐾 = 𝑛=0 𝑛=𝑁−1 𝑥 𝑛 𝑒 −𝑗∗2∗𝜋∗𝐾∗𝑛 𝑁 The power spectrum of a discrete sequence x[n] is given by, Where X(K) is the Discrete Fourier Transform of x[n]
- 26. 12. Windowing techniques used for FIR Filter Design [refer Exercise no.12] *Rectangular window *Hamming Window *Hanning Window *Blackmann Window *Bartlett window
- 27. 13. FIR- Low Pass Filter-Windowing technique [refer Exercise no.13] h[n] = hd [n]*W[n] hd [n] = FIR LPF impulse response W[n] = Hamming window function hd [n] = sin(wc*(n-(N-1)/2)) / (π*(n-(N-1)/2))
- 29. Assignments 1. Generate LPF, HPF, BPF, BSF responses for even length and odd length both symmetric and Asymmetric filter impulse responses. Show that the odd length symmetric FIR filter is suitable for designing all kind of filters such as LPF, HPF, BPF, BSF. 2. Generate Chebyshev IIR digital filter and compare its frequency response characteristics with Butterworth IIR digital filter for the same filter order. 3. Generate Chebyshev IIR digital filter for both odd order and even order. Compare their gain in frequency response characteristics Any Queries regarding assignment problems [email protected]