This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Problem1 Case1 : Step # 1 Defining the signal NPoints N 256 = NPoints N 256 = f s 1000 = Sampling Frequency  Hz f s 1 10 3 × s Hz ⋅ = t 1 f s = f0 20 f s N ⋅ = Analog Input Frequency  Hz f0 78.125 = A p 5 = n N 1 .. = x n A p sin 2 π ⋅ f0 f s ⋅ n π 3 + ⋅ = Input Signal f0 f s N 20 = BIN frequency !! Theoretical rms value !! rms_a A p 2 = rms_a 3.536 = Theoretical total power (rms ^2) value !! rms_a 2 12.5 = 51 102 153 204 255 6 3 3 6 INPUT SEQUENCE Time [ Sample ] Amplitude [ Volts ] x n n Step # 2 Using the new definition of the NPoint DFT of x[n] f n f s N n ⋅ = These are the BIN frequencies [ Hz ] DFT X n N 1 m x m e i 2 π ⋅ N ⋅ m ⋅ n ⋅ ⋅ ∑ = = P1 n 20 log X n ( 29 ⋅ = P_r max P1 ( ) = P2 n P1 n = P1_h n P1 n P_r = 100 200 400 300 200 100 DFT of Input Sequence Discrete Samples Magnitude P1_h n n Step # 3 DFT of WINDOWED SEQUENCE USING HAMMING WINDOW k N 1 .. = X1_hamm k N 1 m x m 0.54 0.46 cos 2 π ⋅ m N 1 ⋅ ⋅ m ≤ N 1 ≤ if 0 otherwise ⋅ e i 2 ⋅ π ⋅ m ⋅ k N ⋅ ⋅ ∑ = = P1_hamm k 20 log X1_hamm k ( 29 ⋅ = P_r_hamm max P1_hamm ( ) = P2_hamm k P1_hamm k = P_r_hamm 50.743 = P1_hamm k P1_hamm k P_r_hamm = 100 200 150 100 50 Normalized DFT of Hamming Window Discrete frequencies Magnitude in db P1_hamm k k Comparing two DFT's 200 400 600 800 1 10 3 × 400 300 200 100 Comparision of DFT sequences Analog Frequency Hz Power in dbW P1_hamm k P1_h k k f s N ⋅ Step 5 : Power Spectral Density Xp n 1 N X n ⋅ = Normalized DFT ∆ f f s N = ∆ f 3.906s Hz ⋅ = P n Xp n ( 29 2 = Power Spectrum (volts ^2) PSD n Xp n ( 29 2 ∆ f = Power Spectral Density (volts ^2 / Hz) 100 200 300 400 500 600 700 800 900 1 10 3 × 1 10 5 × 1 10 4 × 1 10 3 × 0.01 0.1 1 10 Power Spectrum Frequency [ Hz ] Power Spectrum [ volts^2 ] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 10 6 × 1 10 5 × 1 10 4 × 1 10 3 × 0.01 0.1 1 Power Spectral Density Normalized frequency [ unitless ] Power Spectral Desnity [ volts^2 / Hz ] TIME DOMAIN rms CALCULATIONrms value of signal  1 N N 1 m x m ( 29 2 ∑ = ⋅ 3.536 = FREQUENCY DOMAIN rms CALCULATION Summing all power coponents over the frequency spectrum N 1 m Xp m ( 29 2 ∑ = 3.536 =rms value of signal  Area under the curve over the frequency spectrum N 1 m PSD m ∆ f ⋅ ( 29 ∑ = 3.536 =rms value of signal  Step # 5 Estimation of Signal frequency and amplitude PEAK FINDING ALGORITHM !!!...
View
Full
Document
 Fall '09
 Dr.Yang
 Frequency, Signal Processing, spectral density, spectrum analyzer, spectrum, DFT Peak

Click to edit the document details