Use finite-duration windows to model the extraction of a segment from a signal
with a potentially infinite duration
Apply windows to better control resolution and leakage in spectral analysis
Interpret the power spectral density (PSD)
Distinguish PSD, ESD and the mean-square (power) spectrum (MS spectrum),
knowing the cases in which one should be adopted
Estimate PSD, ESD and the mean-square (power) spectrum (MS spectrum) using
the FFT, and be familiar with concepts such as the periodogram and Welch’s
method
Recognize that the periodogram variance does not decrease with the number of
samples, and understand how Welch’s method decreases the variance
Learn how the noise floor decreases with an increased number
of FFT points
Estimate the PSD from the autocorrelation
Distinguish the unilateral and bilateral representations
Perform spectrum analysis with a computer
Be able to mathematically model the spectrum leakage when windowing a signal
via the circular convolution of the original spectrum with the window’s spectrum
Observe that the FFT resolution
improves as
gets larger, but this cannot recover the leakage that occurred due to windowing
Know the Z transform property to easily normalize the samples of an impulse
response
by their summation to have a gain of 0 dB at the DC
Understand the picket fence effect when using FFTs for spectral analysis
Learn the reasons that lead a stronger sinusoid that is not bin-centered to
completely hide a weaker sinusoid in FFT-based spectral analysis
Estimate not only the sinusoid frequency but also its correct amplitude and
correct the window scalloping loss
Distinguish a spectrum analyzer and a vector network analyzer (VNA)
Obtain the output PSD when the input to a LTI system is a wide-sense stationary
(WSS) process with a given input PSD
Model the filtering of white noise through LTI systems
Perform parametric PSD estimation via autoregressive (AR) models