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In implementing an FFT algorithm, it is sometimes useful to generate the powers of WN with a recursive difference equation, or oscillator. In this problem we consider a radix-2 decimation-in-time algorithm for N = 2ν . Figure 9.11 depicts this type of algorithm for N = 8. To generate the coefficients efficiently, the frequency of the oscillator would change from stage to stage. Assume that the arrays are numbered 0 through ν = log2 N, so the array holding the initial input sequence is the zeroth array and the DFT is in the vth array. In computing the butterflies in a given stage, all butterflies requiring the same coefficients Wr N are evaluated before obtaining new coefficients. In indexing through the array, we assume that the data in the array are stored in consecutive complex registers numbered 0 through (N - 1). All the following questions are concerned with the computation of the mth array from the (m-1)st array, where 1 ≤ m ≤ ν. Answers should be expressed in terms of m.
(a) How many butterflies must be computed in the mth stage? How many different coef- ficients are required in the mth stage?
(b) Write a difference equation whose impulse response h[n] contains the coefficients Wr N required by the butterflies in the mth stage.
(c) The difference equation from part (b) should have the form of an oscillator, i.e., h[n] should be periodic for n ≥ 0. What is the period of h[n]? Based on this, write an expression for the frequency of this oscillator as a function of m.
What is the equivalent (total) resistance of 100, 200, and 50 resistors connected in series What is the equivalent (total) resistance of 100, 200, and 50 resistors connected in parallel
(a) Design a half-subtractor circuit with inputs X and Y and outputs D and B. The circuit subtracts the bits X-Y and places the difference in D and the borrow in B. (b) Design a full-subtractor circuit with three inputs X,Y,Zand two outputs D and B..
1A baseband signal with 4 kHz bandwidth is sampled at 1.2 times of its Nyquist sampling rate. Calculate:A. The sampling rate at which this signal is sample.B. The guard frequency band between the repeats of the spectrum.
A sinusoidal voltage has a maximum value of 100V, and the value is 10V at t=0. The period is T=1ms. Determine v(t)
In n-channel JFET, Ohmic region is separated from Saturation region by VP so called Pich-off voltage or VGS(OFF). What is the value if IDand VGS at this location and how we can calculate the value of VP from ID and VGS
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Given the 16-bit operand 00110101 11001010, what operation must be performed and what operand must be used a) to clear all odd bit positions to 0 (Assume bit positions are15 through 0 from left to right.)
If a diode is constructed from doped silicon at concentrations on the N-side of 10^16 atoms/cm^3 and the P-side of 10^15 atoms/cm^3, compute its built-in potential and the width of the depletion region.
An antenna with a radiation resistance of 48 ohms, a lossresistance of 2 ohms, and a reactance of 50 ohms is connected to agenerator with open-circuit voltage of 10 V and internal impedanceof 50 ohms via a λ/4-long transmission line.
An electric dipole consists of a particle with a charge of 6*10^-6C at the origin and a particle with a charge of -6*10^-6C on the x axis at x=3*10^-3m..
IN a 2-pole, 208 V (line-to-line, rms), 60-Hz, motor, Rs= 0.5Ω and R'r = 0.45Ω, Xls= 0.6Ω, and X'tr = 0.83Ω. The magnetizing reactance Xm = 28.5Ω. This motor is supplied by its rated voltages. The rated torque is developed at teh slip s = 0.04.
How much charge is stored in a 5uF capacitor connected across a 70V supply and For a constant supply voltage and an increasing value of capacitance, what is the effect on the amount of charge (Q)? Explain your reasoning.
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