Choose two analog signals and calculate the inner product of these signals.
Choose two analog signals and calculate the inner product of these signals.
t tao are real numbers) is a basis set for the analog complex signal space 1: Show that the set DiracDela(t-tao 2: Choose two discrete signals and calculate the inner product of these signals 3: Choose two analog signals and calculate the inner product of these signals
With examples, explain the two types of signals (Analog and Digital) and two types of data (Analog and Digital). With the above combinations, provide the real life applications and examples for the communication of the above four combinations. (10 marks)
2. Inner Product (Scalar Product) Calculate the inner products of all combinations of two vectors drawn from the set |(1) = (?). (as) = (?). (as) = (i+1) This information is most compactly displayed as a 3 x 3 table. Are the vectors in this set normalized? If not, normalize them.
DILU 2d) Analog and Digital Signals i. A 10-bit linear analog-to-digital has reference voltage 3.3 V such that it operates correct. for input voltage Vin in the range 0 < Vin < 3.3 V. What is its output, in unsigned binary when Vin = 2.267 V? - ii. What is the quantisation error (in volts) for a 10-bit linear analog-to-digital converter with reference voltage 3.3 V?
A piezoelectric pressure transducer is equipped with a charge amplifier that generates analog voltage signals on the output. For further processing of these signals, an engineer is tasked to design an active, inverting, low-pass, 1st-order RC filter. The filter should have a cutoff frequency 6 kHz and a static sensitivity 5.5. The engineer can use only the following components: type-741 operational amplifiers, resistors of any values, and 0.5-microfarad capacitors. (a) Draw the circuit diagram of the active, inverting, low-pass, 1st-order...
Consider R4 as an inner product space with the following inner product : < (a,b,c,d), (e, f, g, h) >= ae + bf + .cg + gdh. Determine all the vectors orthgonal to both (1, 2, 8, 8) and (0,0,4, -8) in this inner product space. Hint: To do this take a general element from R4 and calculate its inner product with both these vectors separately. This should result in a system of two equations which you can then solve.
Q1 Marks: 40 A digital communication system has 96 analog telephone signals, each band limited to 4 kHz. The telephone signals are converted to digital binary data using Pulse Code Modulator (PCM) system, which use a uniform quantiser followed by an 8-bit encoder. The system uses two bits for synchronization. The digital binary data are then time-division multiplexed and transmitted over a single communication channel. Analyse the communication system by considering the following principles: (i) Determine the number of quantization...
An inner produce, such as the dot product, always uses two vectors as operands and produces a scalar number as the result. O True O False
1.(16) Let P be an inner product space with an inner product defined as <.g > Ox)g(x)dx a) Let / =1+x.8=-2+x-x. Compute: <.8 >. The angle between / and g, and proj, b) Let h=1+ mx' in P Find m such that and h are orthogonal c) Let B = (1+x.I-XX+X' is a basis for P. Use the Gram-Schmidt process to covert B to an orthogonal basis for P. 2. Suppose and ware vectors in an inner product space V...
7 Consider the inner product space Co. 11 with the inner product defined by < 2,9 >= ( ( (x) g(x) dx (a) Show that f(x) = 1 and g(x) = 2x - 1 are orthogonal (b) Find ||g(2)|| (e) Find the distance d(f(x), g(x)) between f(x) and g(x)