Signal_Processing

Multiple labs contains our work in treatment of sound signal and image. Language : Python

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Denoising_STFT.ipynb — STFT-Based Audio Denoising

This notebook implements Short-Time Fourier Transform (STFT) based denoising: • STFT computation: Signal is segmented with overlapping windows, and an FFT is applied to each segment to generate a time-frequency spectrogram. This reveals how spectral content evolves over time.  • Noise identification: Noise components are statistically characterized from STFT magnitude, often using thresholding in the time-frequency domain. • Inverse STFT (ISTFT): After noise suppression, the denoised spectrogram is converted back to the time domain by inverse transformation. • Evaluation: A Signal-to-Noise Ratio (SNR) is computed to quantify improvement in signal quality before vs. after denoising (higher SNR indicates better denoising). • Visualization: Spectrogram plots show raw vs. denoised energy distributions over time and frequency.

Key Methods: STFT/ISTFT, windowing, spectrogram thresholding, SNR evaluation.

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Denoising_Wavelet.ipynb — Wavelet Denoising

This notebook explores wavelet domain denoising: • Discrete Wavelet Transform (DWT): The signal is decomposed into multi-scale coefficients capturing both low-frequency approximation and high-frequency details. • Thresholding: Noise tends to dominate high-frequency detail coefficients. Coefficients below a certain threshold are shrunk or zeroed out to suppress noise. • Reconstruction: Denoised signal is obtained by inverse wavelet transform. • Comparison: Performance may be compared with other methods like STFT denoising.

Key Methods: Wavelet transform (e.g., Daubechies or Haar), coefficient thresholding, inverse DWT.

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Filter_FIR.ipynb — Finite Impulse Response Filtering

This notebook demonstrates classical FIR filter design: • Design filters (e.g., low-pass, high-pass) by specifying frequency bands and desired response. • Use numerical methods to compute symmetric FIR coefficients that satisfy the design. • Apply filters to time-domain signals using convolution. • Plot frequency responses (magnitude vs. frequency) and time-domain filtered signals.

Key Methods: FIR filter design, convolution, frequency response analysis.

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Filter_Image.ipynb — Image Filtering

This notebook covers spatial filtering in digital images: • Apply 2D FIR filters for smoothing (blurring) and edge detection. • Use convolution with kernels such as Gaussian blur, Sobel, or custom matrices. • Compare filtered and original images side-by-side. • Analyze effects of different kernel sizes on feature enhancement or suppression.

Key Methods: 2D convolution, image kernels (blur, edge detection), visualization.

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Fourier_Guitar_tuner.ipynb — Audio Pitch Detection

This notebook applies Fourier analysis to musical audio: • Compute FFT of a guitar recording to identify dominant spectral peaks. • Estimate the fundamental frequency to detect the played note. • Compare detected frequency to standard pitch frequencies (e.g., A4 at 440 Hz). • Provide a visually intuitive tuning guide.

Key Methods: FFT, frequency peak detection, pitch estimation.

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Fourier_Zoom_image.ipynb — Fourier Transform for Image Zoom

This notebook uses 2D Fourier Transform to analyze and manipulate images: • Perform 2D FFT on an image to obtain frequency domain representation. • Zero-pad or resample the Fourier spectrum to achieve interpolation/zooming in the spatial domain. • Apply inverse FFT to reconstruct enlarged images.

Key Methods: 2D FFT/IFT, frequency domain interpolation, image reconstruction.

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InverseProblems.ipynb — Inverse Problem Solving

This notebook illustrates reconstruction from indirect observations: • Model measurement process as a linear system (e.g., convolution or blurring). • Apply inverse techniques such as deconvolution, Tikhonov regularization, or pseudoinverse. • Compare reconstructed signals to originals, analyzing artifacts and stability.

Key Methods: Linear inverse problems, regularization, deconvolution.

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fourier.ipynb — Intro to Fourier Transform

This foundational notebook highlights: • Relationship between time and frequency domains via Discrete Fourier Transform (DFT). • Signal reconstruction from Fourier coefficients. • Effects of zero-padding and spectral leakage. • Visualization of magnitude and phase spectra.

Key Methods: DFT/FFT, spectral plots, signal synthesis.