Sampling Frequency fs=400 kHz, Duty Cycle 0.1, Amplitude 2V
Base Frequency fb=10 kHz, Amplitude 2.5 Vtt

1 Time Domain graph 1.1



2 Base Frequency 200 kHz, Sampling Frequency 1500 kHz Frequency Domain graph 2.1


3 Sample frequency 500 kHz, Base Frequency 200 kHz
f0=200kHz f1=300kHz f2=700kHz f3=800kHz f4=1200kHz

The upper and lower sidebands have frequencies of n*fs+fb and n*fs-fb
f0=fb
f1=n*fs-fb ( n=1)
f2=n*fs+fb (n=1)
f3=n*fs-fb (n=2)
f4=n*fs+fb (n=2)

4 Base Frequency 100 kHz
While decreasing the Base Frequency downto 100 kHz the upper and lower sidebands will move closer to their corresponding sample frequency ( n*fs)
f0=100kHz f1=400kHz f2=600kHz f3=900kHz f4=1100kHz



5 Duty Cycle
Change the duty cycle of p(t) so that the amplitude in the frequency spectrum of u(t) is zero at 3*fs
Duty Cycle = 0.3
Amplitude of the spectrum around fs = 0.45 Volt

6 Duty Cycle
Change the duty cycle of p(t) so that the amplitude in the frequency spectrum of u(t) is zero at 2*fs
Duty Cycle = 0.5
Amplitude of the spectrum around fs = 0. 5 Volt

7 By changing the duty cycle of p(t), one is able to define the frequency at which the amplitude of
the sidebands will be zero.
The amplitude of one of the sidebands around n*fs = 2t/Ts * sinc(ft)
Since ft=t/Ts=Duty Cycle is the amplitude given by 2*d*sinc(n*d)

This means that in order to obtain a zero amplitude spectrum around 3*fs, the duty cycle of p(t)
must be 1/3=0.33 wich of course is the same duty cycle as measured at exercise 5.

In order to obtain a zero amplitude spectrum around 2*fs, the duty cycle has to be ½=0.5

The amplitude of the spectra around fs are given by 0.5 * Vbase * Vsample*2*d*sinc(n*d)


8 This exercise is intentionally left blanc by our Practical Training Coordinator

9 Signal Reconstruction




fs=800 kHz and fb=200 kHz, duty cycle = 10 %



During an increase of frequency fb the amplitude of the reconstucted signal decreases due to the filter attenuation of 50 dB / octave.

10 When increasing the base frequency fb up to 600 kHz a new phenomenon is observed : Aliasing or
fold-back distortion.
Fsideband = fs-fb = 800kHz-600kHz = 200 kHz
I.E. a signal appears with a frequency much lower than the original signal fb.
Graph 10.1 : Similar to the graph shown above . ( just a sine-wave )

11 By further increase of fb the phenomenon will repeat again, this happens at a frequency fb = 1000kHz. In fact this phenomenon never disappears but by using equipment operating at 200kHz up to 1.5 Mhz and a sampling frequency fs=800kHz it seems to disapear between fb=600kHz and 1000kHz
fsideband is defined as either the sum or the differential between the sample frequency and the signal frequency.
Therefore fsideband= | fs-fb | = 1000-800 = 200 kHz