Fourier transform. Spectral analysis brief theoretical review fourier analysis

STANDARD TASK FOR LABORATORY WORK №3

1. 
   It is necessary to investigate the spectrum of a finite signal. Obtain the Fourier Transform of the signal. Define Magnitude (Power), Amplitude and Phase for the FFT of the signal. Attach the plot. The shape of the signal depends on individual variant (see Table1).
   

Table 1

Variants	1	2	3	4	5	6	7	8	9
Shape of a finite signal	Triangular pulse	Rectangular pulse	Rectangular pulse	Triangular pulse	Rectangular pulse	Triangular pulse	Rectangular pulse	Triangular pulse	Triangular pulse
Signal property	height 2, centered at 5 instant time, width of 0.8	height 6, centered at 5 instant time, width of 4	height 2.5, centered at 2 instant time, width of 8,	height 5, centered at 20 instant time, width of 6, skew 0	height 1, centered at 9 instant time, width of 6	height 8, centered at 12 instant time, width of 5, skew -0.5	height 12, centered at 5 instant time, width of 8	height 4, centered at 8 instant time, width of 4	height 3, centered at 5 instant time, width of 10, skew 1

Prompt: To generate rectangular signal the following syntax is used:
rectpuls (t,w) returns a continuous, aperiodic, unity-height rectangular pulse at the sample times indicated in array t, centered about t = 0 and with a width of w, by default 1.
For triangular signal generation use command “tripuls”, namely
tripuls (T,w,s) returns a continuous, a periodic, symmetric, unity-height triangular pulse at the times indicated in array t, centered about t=0 and with a width of w (by default 1) and with skew s, where -1 < s< 1. When s is 0, a symmetric triangular pulse is generated.

2. 
   . Define the Fourier Transform for periodic signal. In general, the signal has the following form
   

Initial data for periodic signal and its type is specified in Table 2.
Table 2