Filter Frames of a Noisy Sine Wave Signal in MATLAB

This example shows how to lowpass filter a noisy signal in MATLAB® and visualize the original and filtered signals using a spectrum analyzer. For a Simulink® version of this example, see Filter Frames of a Noisy Sine Wave Signal in Simulink.

Specify Signal Source

The input signal is the sum of two sine waves with frequencies of 1 kHz and 10 kHz. The sampling frequency is 44.1 kHz.

Sine1 = dsp.SineWave('Frequency',1e3,'SampleRate',44.1e3);
Sine2 = dsp.SineWave('Frequency',10e3,'SampleRate',44.1e3);

Create Lowpass Filter

The lowpass FIR filter, dsp.LowpassFilter, designs a minimum-order FIR lowpass filter using the generalized Remez FIR filter design algorithm. Set the passband frequency to 5000 Hz and the stopband frequency to 8000 Hz. The passband ripple is 0.1 dB and the stopband attenuation is 80 dB.

FIRLowPass = dsp.LowpassFilter('PassbandFrequency',5000,...
    'StopbandFrequency',8000);

Create Spectrum Analyzer

Set up the spectrum analyzer to compare the power spectra of the original and filtered signals. The spectrum units are dBm.

SpecAna = spectrumAnalyzer('PlotAsTwoSidedSpectrum',false,...
    'SampleRate',Sine1.SampleRate,...
    'ShowLegend',true, ...
    'YLimits',[-145,45]);

SpecAna.ChannelNames = {'Original noisy signal',...
    'Lowpass filtered signal'};

Specify Samples per Frame

This example uses frame-based processing, where data is processed one frame at a time. Each frame of data contains sequential samples from an independent channel. Frame-based processing is advantageous for many signal processing applications because you can process multiple samples at once. By buffering your data into frames and processing multisample frames of data, you can improve the computational time of your signal processing algorithms. Set the number of samples per frame to 4000.

Sine1.SamplesPerFrame = 4000;
Sine2.SamplesPerFrame = 4000;

Filter the Noisy Sine Wave Signal

Add zero-mean white Gaussian noise with a standard deviation of 0.1 to the sum of sine waves. Filter the result using the FIR filter. While running the simulation, the spectrum analyzer shows that frequencies above 8000 Hz in the source signal are attenuated. The resulting signal maintains the peak at 1 kHz because it falls in the passband of the lowpass filter.

for i = 1 : 1000
    x = Sine1()+Sine2()+0.1.*randn(Sine1.SamplesPerFrame,1);
    y = FIRLowPass(x);    
    SpecAna(x,y);                              
end
release(SpecAna)