Core Signal Processing Concepts and Python Implementation

Digital Signal Processing Fundamentals

Discrete Signal Sampling

Generate continuous sine waves, compare different sampling rates, and analyze aliasing effects.

Quantization Process

Map analog amplitudes to discrete values through analog-to-digital conversion, examine resolution levels, and analyze quantization error and noise.

ADC and DAC Conversion

Implement anti-aliasing filters and oversampling during signal acquisition, reconstruct signals, plot time-domain graphs, and customize processing parameters.

Digital Filter Design

Modify signal frequencies using low-pass, high-pass, band-pass, and band-stop filters. Plot magnitude responses for each type using window method, Parks-McClellan algorithm, and least squares approaches.

Signal Spectrum Analysis

Compute and plot frequency spectra using Fourier series analysis, discrete Fourier transform for frequecny domain analysis, and fast Fourier transform with time decimation techniques. Analyze spectral resolution, leakage, power spectra, and zero-padding methods.

Baseband Wireless Signal Modulation

Implement BPSK, QPSK, and QAM modulation schemes. Evaluate additive white Gaussian noise by measuring signal-to-noise ratio, calculating error vector magnitude and bit error rate. Design pulse shaping and matched filters using square-wave pulses, sinc filters for bandwidth limiting, and raised-cosine filtering.

Complex Frequency Domain Analysis

Demodulate amplitude modulated signals with phase error analysis, perform QAM demodulation using FFT calculations, and implement complex QAM demodulation with visualization.

Frequency Planning

Caclulate nonlinear response effects in amplifier outputs, simulate spurious signals in interleaved ADC systems, and determine alias spur positions.

Dynamic RF User Control

Design RF transmitter and receiver modulation schemes, implement message reception protocols, handle image transmission, and apply forward error correction with parity check matrices using LDPC encoding and soft-decision log-likelihood ratio demodulation.

Generative Adversarial Networks for Signal Processing Testing

Testing Objectives

• Generate and characterize controlled datasets
• Define machine learning model specifications for GAN architecture
• Execute generative models and extract signals using surrogate models

Signal Modeling with Noise

Most signals from electrical/mechanical systems follow sinusoidal patterns:

y = A × sin(ωx) + b

where A represents signal amplitude, ω denotes frequency, and b is the bias offset.

Real-world signals incorporate noise elements, with Gaussian white noise being predominant:

y = A × sin(ωx + b) + B × N(μ, σ)

where μ typically equals 0, σ remains fixed at 1, and B controls noise amplitude.

Parameter Randomization Implementation

Signal parameters with realistic variations:

• Amplitude range: 0.1 to 10 (step: 0.1)
• Bias range: 0.1 to 10 (step: 0.1)
• Frequency range: 1 to 2 (step: 0.001)
• Noise amplitude: fixed at 0.3

import numpy as np
import matplotlib.pyplot as plt

SIGNAL_LENGTH = 300
x_axis = np.linspace(-5, 5, SIGNAL_LENGTH)

def create_signal_sample():
    amplitude_range = np.arange(0.1, 10, 0.1)
    offset_range = np.arange(0.1, 10, 0.1)
    frequency_range = np.linspace(1, 2, 1000)
    
    random_noise = np.random.normal(size=len(x_axis))
    selected_amp = np.random.choice(amplitude_range)
    selected_freq = np.random.choice(frequency_range)
    selected_offset = np.random.choice(offset_range)
    
    signal_output = selected_amp * np.sin(x_axis * selected_freq) + selected_offset + 0.3 * random_noise
    
    parameter_labels = ['Amplitude', 'Frequency', 'Offset']
    parameter_values = [selected_amp, selected_freq, selected_offset]
    parameter_string = parameter_labels[0] + ' ' + str(selected_amp.round(1)) + ' '
    
    for index in range(1, len(parameter_values)):
        parameter_string += parameter_labels[index] + ' ' + str(parameter_values[index].round(1)) + ' '
    
    plt.plot(x_axis, signal_output, '.')
    plt.title(parameter_string)
    plt.xlabel('x')
    plt.ylabel('y')
    return signal_output

Generative Adversarial Network Architecture

The GAN employs conditional generation where the generator creates signals from random noise vectors while the discriminator distinguishes between real and generated samples.

from keras.models import Sequential
from keras.layers import Dense, LSTM
from keras import Input

def build_discriminator(input_size=SIGNAL_LENGTH):
    discriminator_model = Sequential()
    discriminator_model.add(Dense(SIGNAL_LENGTH, activation='relu', input_dim=input_size))
    discriminator_model.add(Dense(250, activation='relu'))
    discriminator_model.add(Dense(100, activation='relu'))
    discriminator_model.add(Dense(1, activation='sigmoid'))
    discriminator_model.compile(loss='binary_crossentropy', optimizer='adam', metrics=['accuracy'])
    return discriminator_model

def build_generator(latent_dim, output_size=SIGNAL_LENGTH):
    generator_model = Sequential()
    generator_model.add(Input(shape=(latent_dim, 1)))
    generator_model.add(LSTM(150))
    generator_model.add(Dense(output_size, activation='linear'))
    generator_model.compile(loss='mean_absolute_error', optimizer='adam', metrics=['mean_absolute_error'])
    return generator_model

def build_gan(generator, discriminator):
    discriminator.trainable = False
    gan_model = Sequential()
    gan_model.add(generator)
    gan_model.add(discriminator)
    gan_model.compile(loss='binary_crossentropy', optimizer='adam')
    return gan_model

The model configuration uses SIGNAL_LENGTH = 300 as the output dimension and latent_dim as the noise vector size.