Study the statistical properties of the output response of a system when the input is wide sense stationary
Input Parameters:
Number of Samples: Use the input field to enter the total number of discrete data points that represent the signal over a certain time period.
Mean: Use the input field to enter the mean value of the signal, which represents its average amplitude.
Variance: Use the input field to enter the variance of the signal, which measures the spread or power of the signal values around the mean.
Channel Impulse Response: Enter the impulse response values or coefficients that describe how the channel affects the transmitted signal.
AR Coefficients: Specify the coefficients for the Auto-Regressive (AR) part of the ARMA model, which defines how past signal values influence the current value.
MA Coefficients: Specify the coefficients for the Moving Average (MA) part of the ARMA model, which defines how past noise terms influence the current value of the signal.
ARMA Coefficients: Specify the coefficients for the ARMA model, which combine both AR and MA effects to define how past signal values and noise terms influence the current value.
Noisy Sinusoidal Parameters: Specify the amplitude and frequency values for the noisy sinusoidal signal if it is selected from the 'Choose Input Type' dropdown.
Steps:
a. When the system is LTI:
1. Generate the WSS Signal:
Click the “Generate WSS” button to create a WSS signal has statistical properties (like mean and autocorrelation) that do not change with time shifts.
2. Generate the Channel Impulse Response:
Click the “Generate CIR” button to generate the impulse response values or coefficients.
3. Generate Output Signal when System is LTI:
Click the “Generate Output” button to perform the convolution of the input WSS signal with the LTI channel coefficients. The resulting signal is the output.
4. Check Auto-correlation for the Input Signal:
Click the “Check Auto-correlation for Input” button to measure the similarity between the input WSS signal and a time-shifted version of itself.
5. Check Auto-correlation for the Output Signal:
Click the “Check Auto-correlation for Output” button to measure the similarity between the output signal and a time-shifted version of itself.
b. When the LTI system is modeled as AR, MA, or ARMA:
1. Generate the WSS Signal:
Click the “Generate WSS” button to create a WSS signal with statistical properties (such as mean and autocorrelation) that do not change with time shifts.
2. View Equivalent Channel Impulse Response:
Click the “Estimate CIR Coefficients” button to generate the equivalent impulse response values or coefficients.
3. Generate Output Signal when System is LTI:
Click the “Generate Output” button to perform the convolution of the input WSS signal with the LTI channel coefficients. The resulting signal is the system output.
4. Check Auto-correlation for the Input Signal:
Click the “Check Auto-correlation for Input” button to measure the similarity between the input WSS signal and a time-shifted version of itself.
5. Check Auto-correlation for the Output Signal:
Click the “Check Auto-correlation for Output” button to measure the similarity between the output signal and a time-shifted version of itself.
