1. بخش دوم

2. magnitude spectrum of x(t),
spectrum (or Fourier spectrum) of x( t ).
magnitude spectrum of x(t),
phase spectrum of x(t).

5. THE FREQUENCY RESPONSE OF CONTINUOUS-TIME LTI SYSTEMS
frequency response of the system
Example:
همانطور که قبلا هم گفته شد باز هم می بینیم تابع ویژه سیستم و H(w0) مقدار ویژه آنست

6. Example:
Example:

7. Example:

8. Example:

10. Fourier Transform Applications

11. FILTERING
Ideal Low-Pass Filter
(LPF)
Ideal High-Pass Filter
(HPF)
(LPF)
(HPF)

12. Ideal Bandpass Filter
(BPF)
Ideal Bandstop Filter
(BSF)
(BSF)
(BPF)

13. Sampling Systems

15. The Sampling Theorem
The extremely useful sampling theorem, also known as the Nyquist theorem, or the Shannon theorem, gives a sufficient condition to recover a continuous-time signal from its samples
Ideal lowpass filter used
to recover the continuous-time signal
from the impulse train sampled signal.

16. Sampling Using a Sample-and-Hold Operator
sample-and-hold (SH)
Simplified sample-and-hold circuit

17. The theoretical representation of a sample-and-hold shown in following Figure
consists
sampling operation (multiplication by an impulse train),
followed by filtering with a linear time-invariant (LTI) system of impulse response h0(t), which is a unit pulse of duration equal to the sampling period Ts.
Note that the sample and-hold operator is sometimes called zero-order-hold (ZOH), although here we call zero-order-hold only the LTI system block with impulse response h0(t) in following Figure .
Effect of sample-and-hold operator on an input signal

18. ZOH system
یادآوری
دیدیم ZOH شامل ضرب قطار ضربه و عبور از فیلتری با پاسخ ضربه مستطیلی بود که مفهوم آن در حوزه فرکانس را بررسی می کنیم:
معکوس این فیلتر برای بازسازی سیگنال مورد نظر است لذا معکوس آنرا می یابیم:

19. Signal reconstruction from the output of the sample-and-hold
Frequency response of the reconstruction filter.