Signal Processing Framework Development 📊📈

This project is a framework for signal processing using Python, designed to help visualize and manipulate signals with various features.

🔲 Task 1 - Signal Processing Framework

Features

1. Reading and Displaying Signals

• Read Samples from a Text File: The framework allows the user to load signal samples from a .txt file.
• Continuous and Discrete Representation: The signal can be displayed in both continuous and discrete-time forms for better visualization and analysis.

2. Signal Generation

• Sinusoidal and Cosinusoidal Signals: Users can generate sinusoidal or cosinusoidal signals with customizable parameters, including:

  • Amplitude (A): Control the height of the wave.
  • Phase Shift (θ): Adjust the phase of the wave.
  • Analog Frequency (f): Set the frequency of the analog signal.
  • Sampling Frequency (fs): Define the sampling rate (must satisfy the sampling theorem).

• The framework includes a Signal Generation menu with two options:

  1. Sine Wave
  2. Cosine Wave

3. Multiple Signal Display

• The framework supports displaying two signals at the same time for comparison and analysis.

🎯Usage

1. Reading Signal Samples from a File: Place your signal samples in a .txt file and load it into the framework to visualize the signal.
2. Generating a Signal:
   • From the menu, choose to generate a sine or cosine wave.
   • Input the required parameters like amplitude, phase shift, and frequency.
3. Simultaneous Signal Display: The framework allows two signals to be displayed at once for a side-by-side comparison.

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🔲 Task 2 - Signal Processing Framework with Arithmetic Operations

Features

1. Arithmetic Operations Menu

• Addition: Add multiple input signals and display the resulting signal.
• Subtraction: Subtract input signals and display the resulting signal.
• Multiplication: Multiply a signal by a constant to either amplify or reduce the signal’s amplitude (invert if the constant equals -1).
• Squaring: Square the signal and display the resulting signal.

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🔲 Task 3 - Signal Quantization

Features

• Quantization of Input Signals: The framework allows the user to quantize a signal by specifying either:

  • Number of Levels: Directly input the levels needed.
  • Number of Bits: The application will compute the appropriate number of levels based on the number of bits.

• Signal Display: The application will display:

  • Quantized Signal: The quantized version of the input signal.
  • Quantization Error: The error between the original and quantized signal.
  • Encoded Signal: The encoded representation of the quantized signal.

🎯 Usage

1. ** Quantize Signals**: Quantize an input signal by selecting the number of levels or bits and visualize the quantization error and encoded signal.

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🔲 Task 4 - Frequency Domain

Features

• Fourier Transform: Apply Fourier transform to any input signal and display frequency versus amplitude and frequency versus phase relations. The user will be prompted to enter the sampling frequency in Hz.

• Modify Signal Components: Allow modification of the amplitude and phase of the signal’s frequency components.

• Signal Reconstruction (IDFT): Reconstruct the signal using Inverse Discrete Fourier Transform (IDFT).

• Save Frequency Components: Save the frequency components of the signal in a .txt file in polar form (amplitude and phase).

• Read Frequency Components: Read a .txt file containing frequency components in polar form and reconstruct the signal using IDFT.

Hint: Due to the similarity between DFT and IDFT, the code should be designed smartly to handle both transformations efficiently.

🎯 Usage

1. Fourier Transform: Input a signal, apply the Fourier transform, and view the frequency domain components (amplitude and phase).
2. Modify Components: Adjust the frequency components and view the updated signal in both time and frequency domains.
3. Reconstruction: Use IDFT to reconstruct the signal from its frequency components, either by computing them or loading from a file.
4. Save & Load: Save the frequency components of the signal in polar form and reload them to reconstruct the signal.

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🔲 Task 5 - Frequency Domain Enhancements

Features

• Discrete Cosine Transform (DCT): Compute the DCT for a given input signal. Display the result and allow the user to choose the first m coefficients to be saved in a .txt file.

• Remove DC Component: Provide the functionality to remove the DC component from the signal.

🎯 Usage

1. Compute DCT: Apply DCT to an input signal, view the result, and save the first m coefficients if desired.
2. Remove DC Component: Process the signal to remove the DC component.

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🔲 Task 6 - Time Domain

Features

1. Smoothing

• Moving Average: Compute the moving average ( y(n) ) for a signal ( x(n) ). The user can specify the number of points to include in the averaging process.

2. Sharpening

• First Derivative: Compute and display the first derivative of the input signal ( Y(n) = x(n) - x(n-1) ).
• Second Derivative: Compute and display the second derivative of the input signal ( Y(n) = x(n+1) - 2x(n) + x(n-1) ).

3. Delaying or Advancing

• Delay or Advance: Shift the signal by ( k ) steps either forward (advancing) or backward (delaying).

4. Folding

• Signal Folding: Fold the signal to visualize its symmetric properties.

5. Delaying or Advancing a Folded Signal

• Delay or Advance Folded Signal: Shift the folded signal by ( k ) steps.

6. Remove DC Component

• DC Component Removal: Remove the DC component of the signal in the frequency domain.

7. Convolution

• Signal Convolution: Convolve two signals to analyze their interaction and combined effect.

🎯 Usage

1. Smoothing: Enter the number of points for averaging to smooth the signal.
2. Sharpening: Compute and display the first and second derivatives of the input signal.
3. Delaying or Advancing: Shift the signal by a specified number of steps.
4. Folding: Fold the signal to view its symmetrical properties.
5. Delaying or Advancing Folded Signal: Adjust the position of the folded signal.
6. Remove DC Component: Eliminate the DC component from the signal in the frequency domain.
7. Convolution: Convolve two signals and view the result.

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🔲 Task 7 - Correlation

Features

1. Correlation

• Normalized Cross-Correlation: Compute the normalized cross-correlation of two signals to measure their similarity and detect any shifts or alignments between them.

2. Time Analysis

• Time Delay Analysis: Perform time delay analysis on two periodic signals. Given the sampling period, approximate the delay between the two signals to understand their temporal relationship.

3. Template Matching

• Template Matching: Allow users to provide paths for two folders of signal classes and a test folder. Using template matching, the application will label all signals in the test folder based on their similarity to the templates provided in the class folders.

🎯 Usage

1. Correlation: Compute the normalized cross-correlation between two signals to analyze their similarity.
2. Time Analysis: Input two periodic signals and the sampling period to estimate the time delay between them.
3. Template Matching: Provide paths for class folders and a test folder, then use template matching to label signals in the test folder.

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🔲 Task 8 - Frequency Domain Enhancements

Features

1. Fast Convolution

• Fast Convolution: Implement convolution using the Fast Fourier Transform (FFT) to efficiently compute the convolution of two signals in the frequency domain. This method speeds up the convolution process compared to the time-domain approach.

2. Fast Correlation

• Fast Correlation: Use the Fast Fourier Transform (FFT) to perform cross-correlation between two signals efficiently. This method enhances performance by leveraging the frequency domain for faster computation.

🎯 Usage

1. Fast Convolution: Apply fast convolution using FFT to quickly compute the convolution of two signals.
2. Fast Correlation: Utilize fast correlation with FFT to efficiently compute the cross-correlation between two signals.

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⭐ Practical Task 1 - Time Domain Enhancements

Features

A. Filtering

• FIR Filters: Implement FIR filters and allow users to specify:

  • Input Signal: The signal to be filtered.
  • Filter Type: Choose from low-pass, high-pass, band-pass, or band-stop filters.
  • Filter Specifications:
    • Sampling Frequency
    • Cutoff Frequency (for low-pass and high-pass filters) or ( f1 ) and ( f2 ) (for band-pass and band-stop filters)
    • Stopband Attenuation ( \delta_s )
    • Transition Band

  The application will:

  1. Choose the appropriate window ( w(n) ) and infinite impulse response ( h(n) ).
  2. Compute the filter order ( N ) and coefficients.
  3. Convolve the input signal with the computed coefficients.
  4. Display the filtered signal.
  5. Save the coefficients to a text file.

  Notes:

  • Adjust frequencies using half the transition band to suit the window method.
  • Normalize frequencies by dividing by the sampling frequency.
  • Ensure coefficients are symmetric and ( N ) is odd.

B. Resampling

• Resampling: Implement resampling with the following options:
  • Upsample: If ( M = 0 ) and ( L \neq 0 ), upsample by ( L ) and apply low-pass filtering.
  • Downsample: If ( M \neq 0 ) and ( L = 0 ), filter first and then downsample by ( M ).
  • Fractional Change: If ( M \neq 0 ) and ( L \neq 0 ), upsample by ( L ), apply low-pass filter, and then downsample by ( M ).
  • Error Handling: If ( M = 0 ) and ( L = 0 ), return an error message.

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⭐ Practical Task 2 - ECG Signal Classification

Features

• ECG Classification: This function distinguishes between two subjects using ECG signals. The application requires:

  • Paths: For two ECG folders of subjects A and B, and a test ECG folder.
  • Sampling Frequency (Fs)
  • Frequency Range: Minimum frequency (( miniF )) and maximum frequency (( maxF ))
  • New Sampling Frequency (newFs)

  The application performs the following steps:

  1. Filter: Apply a band-pass FIR filter with the range ([miniF, maxF]).
  2. Resample: Adjust the signal to newFs if valid, otherwise show an error message and proceed.
  3. Remove DC Component: Eliminate the DC component from the signal.
  4. Normalize: Scale the signal to range from -1 to 1.
  5. Auto-Correlation: Compute auto-correlation for each ECG segment.
  6. Preserve Coefficients: Keep only the necessary coefficients from the auto-correlation.
  7. Compute DCT: Perform Discrete Cosine Transform (DCT).
  8. Template Matching: Compare the non-zero values of the DCT and label each ECG segment in the test folder as subject A or B.
  9. Display: Show the original signal, post-auto-correlation, after preserving coefficients, DCT results, and the final labels for each test case.

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