Filtering Fundamentals

Est. read time: 1 minute | Last updated: July 15, 2025 by John Gentile

Contents

Filter Design
- Estimate Filter Order
FIR Filters
Windowing
Filter Implementation
- Complex-Valued Filters
- References
Parallel/Vectorized Filter/Convolution
References

import numpy as np
from scipy import signal
import matplotlib.pyplot as plt
from rfproto import filter, utils

Filter Design

Estimate Filter Order

One practical estimate comes from fred harris’ rule-of-thumb:

N_{taps} = \frac{\text{Atten}}{22 * B_{T}}

Where:

$\text{Atten}$ is the desired stopband attenuation, in dB.
$B_{T}$ is the normalized transition band, or $B_{T} = \frac{f_{stop}-f_{pass}}{f_{s}}$

FIR Filters

The discrete-time convolution of $M$ filter coefficients with input samples $x[n]$ can be seen as:

y[n] = x[n] * h[n] = \sum_{k=0}^{M-1}h[k]x[n-k]

Picture link

test_filt = filter.fir_filter([0, 0, 1, 0, 0])
for i in range(10):
    print(test_filt.step(i+1))

0.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

Windowing

Window function - Wikipedia: includes list of window functions with example of time and frequency domain responses.

plt.figure()
num_pts = 51
windows = {}
windows['Rectangular'] = signal.windows.boxcar(num_pts)
windows['Hamming'] = signal.windows.hamming(num_pts)
windows['Flattop'] = signal.windows.flattop(num_pts)
windows['Blackman'] = signal.windows.blackman(num_pts)
windows['Blackman-Harris (4-term)'] = signal.windows.blackmanharris(num_pts)

for window in windows:
    A = np.fft.rfft(windows[window], n=2048) / (num_pts/2.0)
    response = np.abs(A / abs(A).max())
    response = 20 * np.log10(np.maximum(response, 1e-10))
    freq = np.linspace(0, 1, len(response))
    plt.plot(freq, response, label=window, linewidth=0.5)
plt.axis([0, 1.0, -120, 0])
plt.ylabel("Normalized Magnitude (dB)")
plt.xlabel(r"Normalized Frequency ($\times\pi$ rad/sample)")
plt.legend()
plt.show()

png

Filter Implementation

Complex-Valued Filters

Rarely you’ll need to use a complex-valued filter- often you’re looking to apply a filter on complex-valued input signals. In this case, the same real filter tap values and convolution process can happen in parallel on both real and imaginary parts of the signal.

Complex Filter Design

References

SciPy Signal - Filter Design Methods

Parallel/Vectorized Filter/Convolution

References

FIR Compiler LogiCORE IP Product Guide • FIR Compiler (PG149) • Reader • AMD Adaptive Computing Documentation Portal