Digital Signal Processing

By the end, you can

• Explain what sampling is and what the sample rate f_s controls.
• Apply the Nyquist–Shannon theorem to compute the minimum sampling rate for a given signal.
• Predict the alias frequency when a tone is under-sampled, and explain why aliasing is irreversible.
• Describe what the Fourier transform reveals and distinguish the time domain from the frequency domain.
• Compare the FFT and the naive DFT in terms of time complexity (O(N log N) vs. O(N²)).
• Distinguish low-pass, high-pass, and band-pass filters by which frequencies each keeps.
• Connect filtering to convolution, and explain why CNN kernels use the same operation.
• Estimate audio dynamic range from bit depth using the 6 dB/bit rule.
• Identify how MP3, JPEG, and noise reduction each exploit frequency-domain processing.