Digital Modulation

A source transmits symbol $S$ that takes values uniformly at random from the set $\{-2,0,2\}$. The receiver obtains $Y=S+N$, where $N$ is a zero-mean Gaussian random variable independent of $S$. The receiver uses the max...

A digital communication system transmits through a noiseless bandlimited channel $[-W, W]$. The received signal $z(t)$ at the output of the receiving filter is given by $z(t) = \sum\limits_{n} b[n]x(t-nT)$ where $b[n]$ a...

A source transmits a symbol $s$, taken from $\\{-4, 0, 4\\}$ with equal probability, over an additive white Gaussian noise channel. The received noisy symbol $r$ is given by $r = s + w$, where the noise $w$ is zero mean...

Let $X(t) = A\cos(2\pi f_0 t+\theta)$ be a random process, where amplitude $A$ and phase $\theta$ are independent of each other, and are uniformly distributed in the intervals $[-2,2]$ and $[0, 2\pi]$, respectively. $X(t...

Consider a channel over which either symbol x A or symbol x B is transmitted. Let the output of the channel Y be the input to a maximum likelihood (ML) detector at the receiver. The conditional probability density functi...

A symbol stream contains alternate QPSK and 16-QAM symbols. If symbols from this stream are transmitted at the rate of 1 mega-symbols per second, the raw (uncoded) data rate is _________ mega-bits per second (rounded off...

Consider a polar non-return to Zero (NRZ) waveform, using +2 V and -2 V for representing binary ' 1 ' and ' 0 ' respectively, is transmitted in the presence of additive zero-mean white Gaussian noise with variance $0.4 \...

A 4 kHz sinusoidal message signal having amplitude 4 V is fed to a delta modulator (DM) operating at a sampling rate of 32 kHz . The minimum step size required to avoid slope overload noise in the DM (rounded off to two...

A message signal having peak-to-peak value of 2 V , root mean square value of 0.1 V and bandwidth of 5 kHz is sampled and fed to a pulse code modulation (PCM) system that uses a uniform quantizer. The PCM output is trans...

In a digital communication system, a symbol $S$ randomly chosen from the set $\left\{s_1, s_2, s_3, s_4\right\}$ is transmitted. It is given that $s_1=-3, s_2=-1, s_3=+1$ and $s_4=+2$. The received symbol is $Y=S+W . W$...

In binary frequency shift keying (FSK), the given signal wave forms are $$\,{u_o}(t) = 5\,\cos \,(20000\,\pi \,t);\,0 \le \,\,t\, \le \,T,$$ and $${u_o}(t) = 5\,\cos \,(22000\,\pi \,t);\,0 \le \,\,t\, \le \,T,$$ where T...

Which one of the following statements about differential pulse code modulation (DPCM) is true?

In a digital communication system, the overall pulse shape p(t) at the receiver before the sampler has the Fourier transform P(f). If the symbols are transmitted at the rate of 2000 symbols per second, for which of the f...

A sinusoidal message signal is converted to a PCM signal using a uniform quantizer. The required signal to quantization noise ratio (SQNR) at the output of the quantizer is 40dB. The minimum number of bits per sample nee...

An ideal band-pass channel 500Hz-2000 Hz is deployed for communication. A modem is designed to transmit bits at the rate of 4800 bits/s using 16-QAM. The roll-off factor of a pulse with a raised cosine spectrum that util...

A speech signal is sampled at 8 kHz and encoded into PCM format using 8 bits/sample. The PCM data is transmitted through a baseband channel via 4-level PAM. The minimum bandwidth (in kHz) required for transmission is ___...

Consider binary data transmission at a rate of 56 kbps using baseband binary pulse amplitude modulation (PAM) that is designed to have a raised-cosine spectrum. The transmission bandwidth (in kHz) required for a roll-off...

A sinusoidal signal of 2 kHz frequency is applied to a delta modulator. The sampling rate and step-size $$\Delta $$ of the delta modulator are 20,000 samples per second and 0.1 V, respectively. To prevent slope overload,...

Consider a binary, digital communication system which uses pulses g (t) and − g (t)for transmitting bits over an AWGN channel. If the receiver uses a matched filter, which one of the following pulses will give the minimu...

A source emits bit 0 with probability $${1 \over 3}$$ and bit 1 with probability $${2 \over 3}$$. The emitted bits are communicated to the receiver. The receiver decides for either 0 or 1 based on the received value R. I...

The modulation scheme commonly used for transmission from GSM mobile terminals is

A sinusoidal signal of amplitude A is quantized by a uniform quantizer. Assume that the signal utilizes all the representation levels of the quantizer. If the signal to quantization noise ratio is 31.8 dB, the number of...

Consider a communication scheme where the binary valued signal X satisfies P{X = + 1} = 0.75 and P {X = - 1} = 0.25. The received signal Y = X + Z, where Z is a Gaussian random variable with zero mean and variance $${\si...

Coherent orthogonal binary FSK modulation is used to transmit two equiprobable symbol waveforms $${s_1}\,(t)\, = \,\alpha \,\,\cos \,\,\,2\,\pi {f_1}\,t\,and\,\,{s_{2\,}}(t)\,\, = \,\alpha \,\,\cos \,\,\,2\,\pi {f_2}\,t$...

The input to a 1-bit quantizer is a random variable X with pdf $${f_x}(x) = 2{e^{ - 2x}}\,\,for\,\,x \ge 0$$ and $${f_x}(x) = 0\,\,for\,\,x\, < \,0$$. For outputs to be of equal probability, the quantizer threshold shoul...

Consider a discrete-time channel Y = X + Z, where the additive noise Z is signal- dependent. In particular, given the trasmitted symbol $$X\, \in \,\{ \, - \,a,\,\, + \,a\} $$ at any instant, the noise sample Z is chosen...

In a PCA system, the signal $$m(t) = \{ \sin (100\,\pi \,t)\, + \cos (100\,\pi \,t\} $$ V is sampled at the Nyquist rate. The samples are processed by a uniform quantizer with step size 0.75 V. The minimum data rate of t...

An M - level PSK modulation scheme is used to transmit independent binary digits over a band-pass channel with bandwidth 100 kHz. The bit rate is 200 kbps and the system characteristic is a raised-cosine spectrum with 10...

The bit rate of a digital communication system is R kbits/s. The modulation used is 32-QAM. The minimum bandwidth required for ISI free transmission is

In a base band communications link, frequencies up to 3500 Hz are used for signaling. Using a raised cosine pulse with 75% excess bandwidth and for no inter-symbol interference, the maximum possible signaling rate in sym...

A binary symmetric channel (BSC) has a transition probability of 1/8. If the binary transmit symbol X is such that P(X =0) = 9/10, then the probability of error for an optimum receiver will be

A BPSK scheme operating over an AWGN channel with noise power spectral density of N 0 2, uses equi-probable signals $$${s_1}\left( t \right) = \sqrt {{{2E} \over T}\,\sin \left( {{\omega _c}t} \right)} $$$ and $$${s_2}\l...

An analog signal is band-limited to 4kHz. sampled at the Nyquist rate and the samples are quantized into 4 levels. The quantized levels are assumed to be independent and equally probable, bit rate is

The amplitude of random signal is uniformly distributed between $$-$$5V and 5V If the positive values of the signal are uniformly quantized with a step size of 0.05 V, and the negative values are uniformly quantized with...

The amplitude of random signal is uniformly distributed between $$-$$5V and 5V If the signal to quantization noise ratio required in uniformly quantizing the signals is 43.5 dB, the step size of the quantization is appro...

A speech signal, band limited to 4 kHz and peak voltage varying between + 5V and - 5V is sampled at the Nyquist rate. Each sample is quantized and represented by 8 bits. If the bits 0 and 1 are transmitted using bipolar...

A speech signal, band limited to 4 kHz and peak voltage varying between + 5V and - 5V is sampled at the Nyquist rate. Each sample is quantized and represented by 8 bits. Assuming the signal to be uniformly distributed be...

A speech signal, band limited to 4kHz and peak voltage varying between +5V and -5V is sampled at the Nyquist rate. Each sample is quantized and represented by 8 bits. The number of quantitization levels required to reduc...

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(t) = {{\sin \,4\,\pi \,W\,t} \over \matrix{ 4\,\pi \,W\,t(1 - 16{W^2}{t^2})...

In delta modulation, the slope overload distortion can be reduced by

Let $$g\left( t \right){\mkern 1mu} {\mkern 1mu} \,\,\,\,\,{\mkern 1mu} = {\mkern 1mu} {\mkern 1mu} p\left( t \right){}^ * p\left( t \right)$$ where $$ * $$ denotes convolution and $$p(t) = u(t) - u(t-1)$$ with $$u(t)$$...

The minimum step-size required for a Delta-Modulator operating at 32 K samples/sec to track the signal (here u(t) is the unit-step function) x(t) = 125t(u(t) - u (t - 1) + (250 - 125t) (u (t - 1) - u (t - 2 )) so that sl...

A symmetric three-level midtread quantizer is to be designed assuming equiprobable occurrence of all quantization levels. The quantization noise power for the quantization region between –a and +a in the figure is

In the output of a DM speech encoder, the consecutive pulses are of opposite polarity during time interval t 1 $$ \le $$ t $$ \le $$ t 2 . This indicates that during this interval

Three analog signals, having bandwidths 1200 Hz, 600 Hz and 600 Hz are sampled at their respective Nyquist rates, enocodes with 12 bit words, and time division multiplexed. The bit rate for the multiplexed signal is

In a PCM system, if the code word length is increased from 6 to 8 bits, the signal to quantization noise ratio improves by the factor

Consider a binary digital communication system with equally likely $$0’s$$ and $$1’s$$. When binary $$0$$ is transmitted the voltage at the detector input can lie between the levels $$-0.25V$$ and $$+0.25V$$ with equal p...

Choose the correct one from among the alternatives A, B, C, D after matching an item from Group 1 with the most appropriate item in Group 2. Group 1. FM 2. DM 3. PSK 4. PCM Group 2 P: Slope overload Q: $${\mu - law}$$ R:...

The input to a linear delta modulator having a step size $$\Delta $$ = 0.628 is a sine wave with frequency f m and peak amplitude E m . If the sampling frequency f s = 40 KHz. the combination of the sine-wave frequency a...

A sinusoidal signal with peak-to-peak amplitude of 1.536V is quantized into 128 levels using a mid-rise uniform quantizer. The quantization-noise power is

A signal is sampled at 8 KHz and is quantized using 8-bit uniform quantizer. Assuming $$SN{R_q}$$ for a sinusoidal signal, the correct statement for PCM signal with a bit rate of R is

If S represents the carrier synchronization at the receiver and $$\rho $$ represents the bandwidth efficiency, then the correct statement for the coherent binary PSK is

For a bit-rate of 8 kbps, the best possible values of the transmitted frequencies in a coherent binary FSK system are

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

In a digital communication system employing Frequency Shift Keying (FSK), the 0 and 1 bit are represented by sine waves of 10 KHz and 25 KHz respectively. These waveforms will be orthogonal for a bit interval of

The input to a matched filter is given by $$$S\left( t \right) = \left\{ {\matrix{ {10\sin \left( {2\pi \times {{10}^6}t} \right),} & {0 < 1 < {{10}^{ - 4}}\sec } \cr {0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\...

The peak-to-peak input to an 8-bit PCM coder is 2 volts . The signal power - to -quantization noise power ratio (in dB) for an input of 0.5 $$\cos \left( {{\omega _m}t} \right)$$ is

In a PCM system with uniform quantization, increasing the number of bits from 8 to 9 will reduce the quantization noise power by a factor of

For a given data rate, the bandwidth B p of a BPSK signal and the band width B 0 of the OOK signal are related as

Compression in PCM refers to relative compression of

The line code that has zero dc component for pulse transmission of random binary data is

The number of bits in a binary PCM system is increased from n to n+1. As a result, the signal to quantization noise ratio will improve by a factor

The signal to quantization noise ratio in an n-bit PCM system

If the number of bits per sample in a PCM system is increased from n to n+1, the improvement in signal-to-quantization noise ratio will be

The bandwidth required for the transmission of a PCM signal increases by a factor of ________ when the number of quantization levels is increased from 4 to 64.

Coherent demodulation of FSK signal can be effected using

The bit stream 01001 is differentially encoded using 'Delay and Ex OR' scheme for DPSK transmission. Assuming the reference bit as a '1' and assigning phases of '0' and '$$\,\pi $$' for 1's and 0's respectively, in the e...

In a BPSK signal detector, the local oscillator has a fixed phase error of 20 0 . This phase error deteriorates the SNR at the output by a factor of

In binary data transmission DPSK is preferred to PSK because

A signal of bandwidth 3.5 kHz has peak-to-peak and rms amplitudes of 4 V and 0.2 V, respectively. This signal is passed through a linear PCM coder and then transmitted over a channel capable of supporting a transmission...

A signal having uniformly distributed amplitude in the interval ( -V, +V ) is to be encoded using PCM with uniform quantization. The signal - to - quantizing noise ratio is determined by the

The message bit sequence input to a DPSK modulator is 1, 1, 0, 0, 1, 1. The carrier phase during the reception of the first two message bits is $$\pi ,\,\,\pi $$. The carrier phase for the remaining four message bits is

A rectangular pulse existing between t = 0 and t = T and having an amplitude A is to be received by a matched filter (a) Draw the impulse response of the matched filter labeling all important points and the axes. (b) Fin...

Companding in PCM systems leads to improved signal - to - quantization noise ratio. This improvement is for