FIR Filter Design for Smoothing Encoder Signals in a Precision Servo Motor

Project info

• Field of studyRobotics and Mechatronics
• LevelUndergraduate thesis (S1)
• Method typeSignal Processing
• Estimated build time± 3 working days
• Toolsfir1, freqz, filtfilt (Signal Processing Toolbox)
• PriceUS$22 - US$138

Research goal

Apply FIR filtering to the encoder position signal to identify the filter cutoff frequency amid quantisation noise through simulation.

Variables

Example result

• 80Filter order
• 100Cutoff (Hz)
• 0.032Passband ripple (dB)
• 60.46Stopband attenuation (dB)
• 2.305SNR before (dB)
• 24.497SNR after (dB)

The order-80 FIR filter with a 100 Hz cutoff raises the signal-to-noise ratio of Encoder position signal from 2.3 dB to 24.5 dB, with 60.5 dB of stopband attenuation suppressing the interference in Quantisation noise.

Computed from illustrative synthetic data, not from a real study.

About FIR Filter Design

A FIR filter has a finite impulse response, is always stable, and can be designed with linear phase. It suits signal filtering that must avoid phase distortion, such as EEG, ECG, and audio.

Steps

1. 1Define the filter type (low-pass, high-pass, band-pass) and cutoff frequency
2. 2Choose the order and window (for example Hamming)
3. 3Design coefficients with fir1
4. 4Check the frequency response with freqz
5. 5Apply with filtfilt for zero phase
6. 6Compare the signal before and after filtering

Assumptions to check

• Cutoff frequencies are normalised to half the sampling frequency
• Order is high enough for a sharp transition (at the cost of delay)
• The signal is long relative to the filter order

Reading and reporting the results

Report type, order, window, cutoff, stopband attenuation, and group delay. Show the frequency response and the effect of the filter on the signal.

Example MATLAB code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

rng(2);
fs = 1000;
filter_cutoff_frequency = (0:1/fs:2-1/fs)';
encoder_position_signal = sin(2*pi*10*filter_cutoff_frequency) + 0.6*sin(2*pi*200*filter_cutoff_frequency) + 0.1*randn(size(filter_cutoff_frequency));

order = 60;
fc = 50;                                           % cutoff in Hz
b = fir1(order, fc/(fs/2), 'low', hamming(order+1));
yf = filtfilt(b, 1, encoder_position_signal);                        % zero-phase filtering

[h, w] = freqz(b, 1, 2048, fs);
att200 = interp1(w, 20*log10(abs(h)), 200);
fprintf('Order %d, group delay %d samples\n', order, order/2);
fprintf('Attenuation at 200 Hz: %.1f dB\n', att200);
fprintf('RMS before: %.3f, after: %.3f\n', rms(encoder_position_signal), rms(yf));

figure;
subplot(2,1,1);
plot(w, 20*log10(abs(h) + eps)); grid on;
xlabel('Frequency (Hz)'); ylabel('Magnitude (dB)'); ylim([-120 5]);
subplot(2,1,2);
idx = 1:500;
plot(filter_cutoff_frequency(idx), encoder_position_signal(idx), filter_cutoff_frequency(idx), yf(idx), 'LineWidth', 1.2);
legend('Raw', 'FIR filtered'); xlabel('Time (s)');

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions