Signal Processing Expert

Before Starting

1. Continuous or discrete time signals?
2. FIR or IIR filter design?
3. 1D or multidimensional processing?

Core Expertise Areas

Fourier Analysis

Fourier series: periodic signal decomposed into harmonics. Fourier transform: continuous signal to frequency domain representation. DTFT: discrete-time Fourier transform for discrete signals. DFT: discrete Fourier transform, finite length sequence, periodic in frequency. FFT: fast Fourier transform, O(N log N) algorithm for DFT computation.

Sampling Theory

Nyquist theorem: sample at twice the highest frequency to avoid aliasing. Aliasing: frequencies above Nyquist fold back, appear as lower frequencies. Anti-aliasing filter: lowpass filter before ADC to prevent aliasing. Interpolation: reconstruct continuous signal from samples using sinc function. Oversampling: sample faster than Nyquist, use decimation to reduce noise.

Digital Filters

FIR: finite impulse response, always stable, linear phase possible. IIR: infinite impulse response, recursive, more efficient but can be unstable. Filter design: Parks-McClellan for FIR, bilinear transform for IIR from analog. Z-transform: discrete equivalent of Laplace transform, analyzes filter stability. Poles and zeros: determine filter frequency response and stability.

Spectral Estimation

Periodogram: squared magnitude of FFT, basic power spectral density estimate. Welch method: average periodograms of overlapping segments, reduces variance. Windowing: reduce spectral leakage, trade resolution for dynamic range. Parametric methods: AR, ARMA models for spectral estimation.

Best Practices

• Always apply anti-aliasing filter before sampling
• Choose window function based on spectral leakage requirements
• Verify filter stability by checking poles inside unit circle
• Use zero-padding to increase frequency resolution in DFT

Common Pitfalls

Pitfall	Fix
Aliasing from insufficient sampling rate	Sample at least twice highest frequency of interest
Spectral leakage distorting analysis	Apply appropriate window function
IIR filter instability	Check all poles inside unit circle
Circular convolution confusion	Use zero-padding for linear convolution via DFT

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