Test: Pulse Modulation

Given,

Also,

Comparing equations (I) and (II), we have:

Thus, the highest frequency component of the given message signal will be

∴ Nyquist rate = 2f_max = 2 x 150 = 300 Hz

PAM, PWM and PPM are examples of analog pulse modulation techniques while PCM is a digital pulse modulation.

Given signal is 


Hence, the maximum frequency present in x(t) is f₁= 2500 Hz
∴ Nyquist rate is given as
f_s = 2f_m
(where, f_m = Maximum frequency present in the signal)
Here, f_m = f₁ = 2500 Hz
∴ Nyquist rate is

Nyquist interval is given as

Let, x(t) = A_m sin (2πf_mt)
The slope of x(t) will be maximum when derivative of x(t) w.r.t. 't' will be maximum.
Maximum slope = Δ/T_s
Hence, for slope overload distortion not to occur,



Hence, slope overload distortion doesn’t occur if 

Given, SNR = 30 dB, n = 10,
Desired value of SNR = 42 dB
With the increase in n by 1 bit, the value of SNR increases by 6 dB. Therefore, to increase the value of SNR by 12 dB, it is necessary to increase n by 2,
∴ n = 10 + 2 = 12
Now, BW of PCM system = 1/2 nf_s
Therefore, BW with n = 10 is

and BW for n = 12 is

Given,

Now, quantization level, q = 2ⁿ
(n = No. of bits/sec)
∴ 2ⁿ = 1024 = 2¹⁰ 
or, n = 10

In practice, the transmitted pulses usually have slightly sloping sides (edges). As the noise is superimposed on them, the width and the position of the regenerated pulses is changed. This distorts the information contents in the PWM and PPM signals. Since PCM does not contain any information in the width or the position of the pulses, therefore PCM has much better noise immunity as compared to PAM, PWM and PPM systems. Hence, both assertion and reason are true and reason is the correct explanation of assertion.

Since, the delta modulation transmits only one bit for one sample, therefore the signaling rate and transmission channel bandwidth is quite small for delta modulation compared to PCM, Hence, assertion is a false statement.
The transmission and receiver implementation is very simple for delta modulation since there is no A/D converter required in delta modulation unlike PCM. Hence, reason is a true statement.