## 1. A 1.0 kHz signal is flat top sampled at the rate of 1800 samples/sec and the samples are applied to an ideal rectangular LPF with cut-off frequency of 1100 Hz, then the output of the filter contains

## 2. A 4 GHz carrier is DSB-SC modulated by a low pass message signal with maximum frequency of 2 MHz. The resultant signal is to be ideally sampled. The minimum frequency of the sampling impulse train should be

## 3. Increased pulse width in the flat top sampling, leads to

## 4. A video transmission system transmits 625 picture frames per second. Each frame consists of a 400 × 400 pixel grid with 64 intensity levels per pixel. The data rate of the system is

## 5. The raised cosine pulse p(t) is used for zero ISI in digital communications. The expression for p(t) with unity roll-off factor is given by $$p\left( t \right) = \frac{{\sin 4\pi \omega t}}{{4\pi \omega t\left( {1 - 16{\omega ^2}{t^2}} \right)}}.$$ The value of p(t) at $$t = \frac{1}{{4\omega }}$$ is

## 6. A sinusoidal signal of 2 kHz frequency is applied to a delta modulator. The sampling rate and step-size Δ of the delta modulator are 20,000 samples per second and 0.1 V, respectively. To prevent slope overload, the maximum amplitude of the sinusoidal signal (in Volts) is

## 7. Coherent orthogonal binary FSK modulation is used to transmit two equiprobable symbol waveforms s_{1}(t) = αcos2πf_{1}t & s_{2}(t) = αcos2πf_{2}t_{1} where α = 4 mV. Assume an AWGN channel with two-sided noise power spectral density $$\frac{{{N_0}}}{2} = 0.5 \times {10^{ - 12}}W/Hz.$$ Using an optimal receiver and the relation $$Q\left( v \right) = \frac{1}{{\sqrt {2\pi } }}\int\limits_v^\infty {{\theta ^{\frac{{{u^2}}}{2}}}du,} $$ the bit error probability for a data rate of 500 kbps is

_{1}(t) = αcos2πf

_{1}t & s

_{2}(t) = αcos2πf

_{2}t

_{1}where α = 4 mV. Assume an AWGN channel with two-sided noise power spectral density $$\frac{{{N_0}}}{2} = 0.5 \times {10^{ - 12}}W/Hz.$$ Using an optimal receiver and the relation $$Q\left( v \right) = \frac{1}{{\sqrt {2\pi } }}\int\limits_v^\infty {{\theta ^{\frac{{{u^2}}}{2}}}du,} $$ the bit error probability for a data rate of 500 kbps is