Consider a different real, discrete-time, LTI system whose impulse response is h[n] and whose Fourier transform is H(Ω). The input to this system is g[n], a

1.5

second white noise signal with a Gaussian amplitude distribution. The output is g_F [n] the filtered version of g[n], that is, g_F [n] = h[n] ⊗ g[n].

1. Is the stochastic signal g_F [n] a “white” noise signal? Explain your reasoning.


2. Based upon the data presented, what type of filter is h[n]: a lowpass filter, a highpass filter, a bandpass filter, or a band-reject filter?


3. When you listen to each of the signals, does this support your answer to the previous question?


4. Both g[n] and g_F [n] have been normalized after analysis but before being converted to audio WAV files. Do they sound equally loud? If not, can you think of an explanation? (Full disclosure: They do not sound equally loud to this author.)


5. How do you explain the change in the estimates of the probability density function between g[n] and g_F [n]?


6. Filters are frequently described as one-pole filters or two-pole filters or three-pole filters, and so forth. How many poles does the filter h[n] have?

Proceeed to another part of this exercise by choosing the variant below.