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Exercise 1.1 Means and Variances of Random SignalsThree different signals: Gaussian distributed noise, uniformly distributed noise and Random binary sequence.

Exercise 1.1 Means and Variances of Random SignalsMean of the Gaussian is 0, uniform noise from -1 to 1, and offset binary noise is 0. Modify mean of the Gaussian to 2, uniform noise from 2 to 4, and offset binary noise to 2.

Exercise 1.2 Generating Probability Density FunctionsProbability density functions of uniform, gaussian noise. Total 1000 samples and number of bins is 40.

Exercise 1.2 Generating Probability Density FunctionsIncrease the no. of samples to 10000 and increasing the total number of bins to 100.

Exercise 1.3 Varying the Mean and Variance of Gaussian Noise SourcesChange the mean of Gaussian to 2 and standard deviation is 1, the range of uniform noise from 1 to 3.

Exercise 1.4 Gaussian Random VariablesThe probability density function (pdf) of a Gaussian random variable.

Exercise 1.8 Resistor Capacitor (RC) FilterImpulse and pulse width response of RC circuit, FFT of the impulse and pulse width response .

Exercise 1.8 Resistor Capacitor (RC) FilterFFT of the filtered noise and of the impulse response.

Exercise 2.1 Aliasing Frequency CalculationFs =32Hz < 2fm =50Hz, which aliasing occurs. Spectrum signal source around 25Hz, samples signal around 7Hz.

Exercise 2.1 Aliasing Frequency CalculationWhen the sampling rate fs>=2fm = 50Hz then signal can recover precisely. In picture below fs=75Hz.

Exercise 2.2 Reconstruction of Sampled SignalsSignal input and the reconstructed signals equal.

Exercise 2.2 Reconstruction of Sampled SignalsSignal input and reconstruct waveform is nearly perfect.Sample rate greater than 10Hz to avoid aliasing.

Exercise 2.5 Quantization Noise Quantizer using uniform noise as an input, the data is quantized into 4 bits or 16 levels.

Exercise 2.5 Quantization Noise

In analysis = 1.53.10-3. Different is by samples of simulate limit. A bit quantizer add then quantization noise power reduce 6dB.Numbers bits of quantization are required for the average quantization noise power to be 96 dB down below the peak signal power 96/6 = 16bit.

Exercise 3.1 Transmitting ImpulsesData rate is set to 2400 bits/sec, bandwidth requires for transmit Impulses very large.

Exercise 3.2 Square Pulse ShapingUse a Pulse Shaping Filter, whereby prior to transmission the data (impulses) will be shaped to be square pulses.Bandwidth requires for transmit is reduces.

Exercise 3.2 Square Pulse ShapingIncrease the number of samples to 8192, spectra of the square pulse waveform which should now be smoother and around low frequency.

Exercise 3.3 Return to Zero Square Pulse ShapingData rate is 2400bps, sampling rate was 96000Hz. Numerator coefficient of filter is 20, thus the duration of the impulse response of this filter is 20\96,000 second.

Exercise 3.4 Recovering Data by SamplingDelay to set sampling instant to middle of a pulse.

Exercise 3.5 Data in a Noisy ChannelNoise source with a standard deviation is 2.5e-3, no bit errors occur.

Exercise 3.5 Data in a Noisy ChannelIncrease the channel Gaussian noise to a standard deviation of 2.5e-2. Some bit errors occurring now.

Exercise 3.5 Data in a Noisy ChannelIncrease the no. of samples to 40000 (1000 bit data), have 150 bit errors is get.Increase the channel noise to a standard deviation of 2.5e-1. BER is above 400 bit errors.

Exercise 3.7 Bit Error Rate in a Gaussian Noise ChannelAWGN with a standard deviation is 25e-2. P(error) =0.15, hence over 100 bits we note 100 x 0.15 = 15 errors.

Exercise 3.7 Bit Error Rate in a Gaussian Noise ChannelIncrease the number of samples to 40000 (1000 bit), about 150 bit error is occur. 1000 x 0.15 =150 theoretical.

Exercise 3.7 Bit Error Rate in a Gaussian Noise ChannelIncrease the standard deviation of the noise to 1/20, run 40000 samples (1000 bits). 300 bit error is get.

Exercise 3.9 Binary Signalling UNIPOLAR NRZ then bit 1 represent by voltage +V and bit 0 by voltage 0V. POLAR NRZ bit 1 represent by voltage +V and bit 0 by voltage V.

Exercise 3.9 Binary SignallingSpectrum UNIPOLAR RZ is large than.

Exercise 3.11 Sinc Pulse ShapingThe data impulses at the rate of 2400 bits/sec are shaped by a sinc pulse, no intersymbol interference occurring.

Exercise 3.11 Sinc Pulse ShapingIncrease the number of samples to 16384, bandwidth is around 1200 Hz.

Exercise 3.13 Raised Cosine Pulse ShapingThe data impulses at the rate of 2400 bits/sec, raised cosin pulse has = 1. No intersymbol interference occur.

Exercise 3.13 Raised Cosine Pulse ShapingIncrease the number of samples to 16384, bandwidth is now 2400 Hz.

Exercise 3.13 Raised Cosine Pulse ShapingChange the roll-off parameter = 0.2, bandwidth is reduced.

Exercise 4.1 Basic Bandpass ModulationDouble-sideband suppressed carrier (DSB-SC) amplitude modulation. Spectrum of modulation signal consist double sideband 99KHz and 101KHz.

Exercise 4.1 Basic Bandpass ModulationChange the input baseband signal to a frequency sweep of 100Hz to 2000Hz over a period of 10msecs. Spectrum of baseband input around low frequeny, of modulation signal around 100KHz.

Exercise 4.2 Basic Quadrature Modulation Two signals multiplexes onto a single carrier, and then demodulates and low pass filters to produce the two signals at the receiver.

Exercise 4.2 Basic Quadrature Modulation Put a small phase error of 4 degrees then demodulate is not precise and will add noise.

Exercise 4.2 Basic Quadrature Modulation For the IQ-mixer, set the IQ rotate parameter to 4 degrees. Effect is the same as putting a phase shift on the carrier as done above.

Exercise 4.3 8 Phase Shift Keying (PSK)The token BER counts the number of errors Ne over the number of trials No, and outputs a value equal to the number of errors divided by the number of trials (Ne/No).

Exercise 4.3 8 Phase Shift Keying (PSK)Increase the value of the noise source to 1e-4W/Hz, then Ne/No unlike 0 approximate 2.8e-1. Constellation I/Q in output scattering.

Exercise 4.4 8 Phase Shift Keying (PSK) Bit Error Rate ExerciseGray encoding is a procedure for ensuring that nearest-neighbor symbol errors only produce one bit error.

Exercise 4.5 Design of a QPSK System Change the phase of the carrier frequency to 10 deg.

Exercise 9.1 Minimum Shift Keying (MSK)Modulation of the NRZ data via a FM (VCO) modulator.

Exercise 9.3 Offset QPSK ExampleMaximum phase shift in QPSK is 180deg and in OQPSK is 90deg.

Exercise 9.3 Offset QPSK ExampleSpectrum of QPSK is large than OQPSK.

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