Fourier Transform 

Period

Increasing the period to infinity changes a periodic signal to a non periodic signal

Repeating a non periodic signal with a period changes it to a periodic signal

Finding the Fourier series of a periodic signal with its period tending to infinity

• The Spectrum Shape remains the same

• The Spectrum gets denser i.e frequency spacing gets smaller

• The magnitude of the spectral lines decrease

False its dependent on the width of the pulse and multiples f = m/tao

The spectrum of it Forward FT shrinks with an increase in the pulse of the signal

A impulse in the FT

Linearly the phase of its spectrum and the magnitude is not affected

true - symmetric amplitude and odd symmetric phase

Fourier series

Sampler, Quantizer and Coder

False, The sampler ensure Discrete time while the quantizer ensures discrete values - Quantized signal.

It encodes the quantized signal to digital input, 0101. It can use a variety of codes to represents quantized signal

To prevent Overlapping .

if w_s >= 2w_n , w_s - w_n >= 2w_n- w_n → w_s - w_n >= w_n . This ensures no overlapping within the spectrum . if w_s <= 2w_n then w_s - w_n <= w_n → Overlapping

Aliasing. Occurs when w_s <= 2w_n

if a signal x(t), is band-limited with X(w) = 0 if |w| > w_n , then x(t) is uniquely determined by its samples, x(n) = x(nT) provided that w_s >=2w_n

2w_n ,The minimum sampling frequency needed to avoid aliasing and f_n is the maximum frequency that is resolved when sampling at the Nyquist rate

The bandwidth of the signal is used as the Nyquist Frequency.

f_s >= 2B given that B = f_max - f_min

prior to sampling and when the sampling Rate is fixed

its an analogue lowpass filter with cut-off frequency = fn (Nyquist Frequency). Bandlimits the analogue input signal to the Nyquist Frequency → fs/2 = fn.

Digital Camera

The resolution of a camera is fixed and the sampling frequency of an imaging sensor is dependent on the resolution of the imaging sensor. The number of pixels that can be captured.

The bandwidth of the input analogue signal can vary. Many camera use an Optical Low Pass Filter to reduce bandlimit the imaged scene below the Nyquist frequency,

There is overlapping at higher frequencies where the changes in colour occur at a lower pixel rate

is a visual perception that occurs when viewing a set of lines or dots that is superimposed on another set of lines or dots, where the sets differ in relative size, angle, or spacing

A pattern that occurs when aliasing occurs showing high frequencies overlapping lower frequencies

Fundamental Frequency range where the frequency of the CT signal when sampled at a rate fs must be within the range -fs/2 <f<

when W = pi and when F = 1/2

-fs/2<f<fs/2

-1/2<F< f

Digital frequency or Discrete Time Frequency

F = f/fs where fs is the sampling frequency

Passing the digital output signal through an interpolator. The interpolator estimate values of continuous time signal for an intermediate values of time

Passing the spectrum through a band limiting filter with its cut of frequency the same as the fundamental frequency of the

Sinc function

multiplying the spectrum of the ideal reconstruction filter with the spectrum of the sampled sign

convolving the sinc function and a train of impulses (the sampled signal)

The sinc function has an infinite length and therefore other discrete time points are affected

Sample and hold - This involves holding the impulses in the time domain for a particular duration ensuring that consecutive discrete points are not affected.

They are convolved in the time domain with the sinc function and in frequency domain multiplies by the lowpass filter

Smoothens edges of sample & hold operation

Attenuates high frequencies let through by sample & hold filter in frequency domain

Normalised by a factor T

Sampling frequency

True