1.  You perform the FFT of 1000 samples collected at 1000 Hz.  When you create the FFT magnitude plot, there are 501 elements in the plot, at 501 different frequencies.  Call this array FFTmag(1:501).  (Using the Matlab convention of lowest index = 1).  

(a) What is the lowest frequency represented (at FFTmag(1))?  In Hz.
Ans:  0 Hz. (DC)  
(b) What is the highest frequency represented (at FFTmag(501))?  In Hz. 
Ans:  Nyquist frequency, 500 Hz.
(c) What is the frequency spacing between plot samples, in Hz?
Ans:  fs/N = 1 Hz.

2.  Draw the frequency magnitude response of a notch (bandstop) filter.  The sampling frequency is 800 Hz.  The -6 dB points are at 80 Hz and 120 Hz.  Your horizontal axis should be linear in frequency, from 0 Hz to the Nyquist frequency.  Indicate the Nyquist frequency in Hz.
Ans:  Approximate gain of 1 (0 dB) at low frequency, dipping to -6 dB at 0.2 fN and continuing to dip to a minimum at 0.25 fN, and rising back to -6 dB at 0.3 fN and then staying close to 0 dB at higher frequencies.  fN = Nyquist freq = 400 Hz. 

3.  Consider an FIR filter z(k) = 5*x(k) + 3*x(k-1) + 2*x(k-2).

(a) What is the order of this filter?
Ans:  2
(b) What is the impulse response of this filter?
Ans:  An impulse input is x(0)=1 and x(k)=0 for all other k.  So z(0)=5, z(1)=3, z(2)=2, and all other z(k) are zero.