{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# Mathcad - DSPtakehomequiz - hz:= 1 1 Design a FIR bandpass...

This preview shows pages 1–5. Sign up to view the full content.

hz 1 = 1- Design a FIR bandpass filter using rectangular, blackman and chebychev windows to satisfy the following specifications --- fs = 1000 Hz, center at 100 Hz, with bandwidth (pass band) of 20 Hz , stopband attenuation > 20 dB is acceptable Pass band ripple is a dont care specification. stop bands starts 20 Hz away from center frequency. which is the best design and why ? analog frequencies f center 100 = f stop1 80 = f s 1000 = f pass1 90 = f stop2 120 = f pass2 110 = Digital frequencies: ω center 2 π f center f s = ω center 0.628 = Radians/Sample !!!! ω pass1 2 π f pass1 f s = ω pass1 0.565 = ω pass2 2 π f pass2 f s = ω pass2 0.691 = ω stop1 2 π f stop1 f s = ω stop1 0.503 = ω stop2 2 π f stop2 f s = ω stop2 0.754 =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
ω c1 ω pass1 ω stop1 + 2 = ω c1 0.534 = ω c2 ω pass2 ω stop2 + 2 = ω c2 0.723 = To determine the number of the filter coefficients the transition bandwidth,stopband attenuation is required δ stop 25 = ∆ω ω pass1 ω stop1 - = ∆ω 0.063 = M 1 0.92 π ∆ω = considering the highest even number of coefficients 0.92 M π transition band rectangular M 1 46 = M 1 57 = DEFINING THE BANDPASS FILTER IMPULSE RESPONSE h bpf n ( ) sin ω c2 n ( 29 n π sin ω c1 n ( 29 n π - n 0 if ω c2 π ω c1 π - n 0 = if = n M 1 - M 1 .. = w r n ( ) 1 =
100 - 50 - 0 50 100 0.999 0.9995 1 1.0005 1.001 Rectangular Window Samples Window coefficients w r n ( ) n n M 1 - M 1 .. = hh bpfr n ( ) w r n ( ) h bpf n ( ) = 100 - 50 - 0 50 100 1 - 0.5 - 0 0.5 1 Multiplication of rect window and bpf Samples Coefficients hh bpfr n ( ) n Computing the DTFT of the windowed bandpass filter N P 3000 = i 0 2N P 1 - .. = ω i i 2 π N P =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
H bpfr ω ( ) M 1 - M 1 n hh bpfr n ( ) ( 29 e i - ω n = = Hbpdf i H bpfr ω i ( 29 = 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.12 0.24 0.36 0.48 0.6 0.72 0.84 0.96 1.08 1.2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 25

Mathcad - DSPtakehomequiz - hz:= 1 1 Design a FIR bandpass...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online