FIR Filters & Convolution

Time-domain and FFT-based convolution, moving-average filters, and general FIR filtering.

pyminidsp.convolution_num_samples(signal_len, kernel_len)

Compute the output length of a full linear convolution.

Compute the output length of a full linear convolution. For input length N and kernel length M, the result is N + M - 1.

pyminidsp.convolution_time(signal, kernel)

Time-domain full linear convolution.

Returns:

numpy array of length signal_len + kernel_len - 1.

Time-domain full linear convolution (direct sum-of-products).

\[\text{out}[n] = \sum_{k=0}^{M-1} \text{signal}[n-k] \cdot \text{kernel}[k]\]

with out-of-range signal samples treated as zero.

Parameters:

• signal – Input signal.

• kernel – FIR kernel.

Returns:

Array of length len(signal) + len(kernel) - 1.

pyminidsp.moving_average(signal, window_len)

Causal moving-average FIR filter.

Returns:

numpy array of the same length as the input.

Causal moving-average FIR filter with zero-padded startup.

\[\text{out}[n] = \frac{1}{W} \sum_{k=0}^{W-1} \text{signal}[n-k]\]

where out-of-range samples (n - k < 0) are treated as zero.

Parameters:

• signal – Input signal.

• window_len – Moving-average window length (must be > 0).

Returns:

Array of the same length as the input.

pyminidsp.fir_filter(signal, coeffs)

Apply a causal FIR filter with arbitrary coefficients.

Returns:

numpy array of the same length as the input.

Apply a causal FIR filter with arbitrary coefficients.

\[\text{out}[n] = \sum_{k=0}^{T-1} \text{coeffs}[k] \cdot \text{signal}[n-k]\]

with out-of-range signal samples treated as zero.

Parameters:

• signal – Input signal.

• coeffs – FIR coefficients.

Returns:

Array of the same length as the input.

pyminidsp.convolution_fft_ola(signal, kernel)

Full linear convolution using FFT overlap-add.

Returns:

numpy array of length signal_len + kernel_len - 1.

Full linear convolution using FFT overlap-add. Produces the same output as convolution_time() but is faster for longer kernels by processing blocks in the frequency domain.

Parameters:

• signal – Input signal.

• kernel – FIR kernel.

Returns:

Array of length len(signal) + len(kernel) - 1.