دوم بخش

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

phase spectrum of x(t).

THE FREQUENCY RESPONSE OF CONTINUOUS-TIME LTI SYSTEMS

frequency response of the system

Example:

و سیستم ویژه تابع بینیم می هم باز شد گفته هم قبال که H(w0)همانطورآنست ویژه مقدار

Example:

Example:

Example:

Example:

Fourier Transform Applications

FILTERING

Ideal Low-Pass Filter (LPF)

Ideal High-Pass Filter (HPF)

(LPF) (HPF)

Ideal Bandpass Filter

(BPF)

(BPF)

Ideal Bandstop Filter

(BSF)

(BSF)

Sampling Systems

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

The Sampling Theorem

Ideal lowpass filter usedto recover the continuous-time signalfrom the impulse train sampled signal.

Sampling Using a Sample-and-Hold Operator

sample-and-hold (SH)

Simplified sample-and-hold circuit

The theoretical representation of a sample-and-hold shown in following Figure consists a) sampling operation (multiplication by an impulse train), b) 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

ZOH systemیادآوریضرب ZOHدیدیم شامل

فیلتری از عبور و ضربه قطاربود مستطیلی ضربه پاسخ با

حوزه در آن مفهوم کهمی بررسی را فرکانس

کنیم:

بازسازی برای فیلتر این معکوسلذا است نظر مورد سیگنال

: یابیم می آنرا معکوس

Signal reconstruction from the output of the sample-and-hold

Frequency response of the reconstruction filter.