Time-Frequency Analysis of Noisy Speech Signals with Denoising and Reverberation Processing

In this document, we will perform the following sequential steps to process noisy speech signals:

1. First, we will conduct time-frequency analysis of the noisy speech signal using methods like spectrogram analysis and power spectral density estimation. This involves MATLAB implementations using functions such as spectrogram() and periodogram() to understand the signal's frequency distribution over time and identify noise components.

2. Next, we will design appropriate digital filters for denoising processing. This includes designing FIR or IIR filters using filter design tools (fdesign, butter, cheby1) with specific frequency response characteristics to eliminate noise while preserving speech components. The implementation will involve frequency response analysis and filter coefficient calculation.

3. After denoising processing, we will perform time-frequency analysis again on the cleaned signal using the same analytical methods. This comparative analysis allows us to evaluate denoising effectiveness through metrics like SNR improvement and visual inspection of spectrogram differences.

4. Finally, we will design a reverberation effect system implementing four comb filters and two all-pass filters in cascade configuration. The comb filters create delayed repetitions for echo generation, while all-pass filters maintain phase characteristics. An equalizer module will be integrated using biquad filter structures to adjust echo timbre and intensity parameters through frequency band gain control.