FILTER Digital Khairul handono

Dedicated hardware processor Frequency Translate Digital Filter 512 Point FFT x(n) X(f) Frequency Translate Digital Filter 1024 Point FFT X(f) Dedicated hardware processor Data Select Filter Select Data Select FFT Select Data Select Data Buffers Digital Filter Data Buffers FFT Data Buffers x(n) X(f) Micro programmable signal processor hardware

Programmable Signal Controller Data Storage x(n) Programmable S P Input/ Output X(f) Distributed Programmable Data Storage Data Storage x(n) Input/ Output X(f) Data Communication Controller x(n) Input/ Output X(f) Processing element Processing element

Converting analogue signals to digital

In the process of measuring the signal, some information is lost.

Aliasing

The high frequency signal is sampled just under twice every cycle

The high frequency signal is sampled twice every cycle

Antialiasing

The Impulse respons of the reconstruction filter has a clasic : sin (x)/ x shape

Quantisation

An analogue signal which is held on the rising edge of a clock signal

Block Diagram

Spectrum

Sistematika Disain Analisis Diskrit Transformasi Z Finite Regst DSP Linier Sistem Diskrit Infinite Impulse Respons Digital Filter Finite Impulse Respons Digital Filter Multirate DSP FFT DFT Adaptive Filter Disain Digital signal

Methodology System Design Step 1 User/customer driven Develop system level Signal processing Non signal processing System level documentation Requirement specification Interface design specification System Requirements Defiition Step 2 Signal Analysis Step 3 Define input signal Types Parameter Noise sources & distribution Data rates Sisgnal Processing Design Step 4 Resource Analysis Dev SP graphs for each procss Specify primitive operation Initial partitioning Arithmetic analysis Iterative process Results in architecture approach Acceptable No Yes Step 5 Configuration Analysis Final partitioning of process Memory, Control, bandwidth Acceptable Perform resource analysis Configuration HW No Yes

Infinite Impulse Response (IIR) Disain prosedure: Menggunakan formula disain untuk analog yaitu penentuan pole dan zero pada Butterworth, Chebyshev dan Elliptic Formula transformasi bidang frekuensi Transformasi bilinier, dg pemetaan pole pada bidang-s ke pole bidang-z

LPF Digital dan Analog

HPF LPF BSF BPF

Keuntungan Digital Filter Stabil thd Panas: Perubahan temperatur pada R,C dan L tidak terjadi, karena menggunakan Adders, multipliers, dan sift registers Presisi: akurasi, stabilitas, respons frekw.dg menggunakan processor register. Mudah Penyesuaian: dapat lebih tepat dan dapat diprogram sesuai kebutuhan Kelipatan: dapat dilipatkan untuk mendapatkan rangkaian yang lebih efisien.

Kerugian Digital Filter Bandwidth terbatas: dengan hasil proses sampling dari analog ke digital (A/D converter), bandwidth signal terbatas setengah dari frekuensi sampling. Keterbatasan register: implementasi sistem waktu diskrit pada perangkat keras dengan penggunaan khusus terjadi penurunan performance, karena terbatasnya jumlah bit.

Sistem Waktu Diskrit

Fungsi Transfer orde-N Inverse Z-tranforms

Lowpass Butterworth Filters

Respons Frekuensi

Analog Lowpass Chebyshev Filter

Analog Lowpass Elliptic Filter

Transformasi Band Frekuensi Design normalized analog filter of order N Perform Freq. Band Transformation analog to analog Desired Digital Filter Digitize filter Design normalized analog filter of order N Perform Freq. Band Transformation analog to analog Desired Digital Filter Digitize filter

Transformasi Bilinier

Pemetaan Frekuensi dari transformasi bilinier

Digital Lowpass Filter Disain

Lowpass transfer function

LPF First order

Butterworth Low Pass Filter fp = 500 Hz fs = 750 Hz Ap = 0.1737 dB As = 40 dB Ap As fp fs

S-plane Pole dan Zero Z-plane Pole dan Zero Zero Pole No. Real Imaginary Real Imaginary 1 0.00000 0.00000 - 0.1564345 0.9876885 2 0.00000 0.00000 - 0.4539906 0.8910065 3 0.00000 0.00000 - 0.7071068 0.7071067 4 0.00000 0.00000 - 0.8910066 0.4539905 5 0.00000 0.00000 - 0.9876884 0.1564344 Z-plane Pole dan Zero Zero Pole No. Real Imaginary Real Imaginary 1 -1.0000 0.00000 + 0.1370099 + 0.844767 2 -1.0000 0.00000 + 0.1092149 + 0.607474 3 -1.0000 0.00000 + 0.0931414 + 0.411143 4 -1.0000 0.00000 + 0.0841441 + 0.238471 5 -1.0000 0.00000 + 0.0800774 + 0.078200

Koefisien orde 2 Numerator Denominator Stage A1 A2 B1 B2 1 2.00000 1.00000 - 0.2740197 0.7324039 2 2.00000 1.00000 - 0.2184297 0.3809528 3 2.00000 1.00000 - 0.1862828 0.1777139 4 2.00000 1.00000 - 0.1682881 0.0639486 5 2.00000 1.00000 - 0.1601547 0.0125276 IIR NORMALIZING FACTOR : C0 = 0.00125 STAGE 1 NORMALIZING FACTOR: C1 = 0.11360 STAGE 2 NORMALIZING FACTOR: C2 = 0.25799 STAGE 3 NORMALIZING FACTOR: C3 = 0.32522 STAGE 4 NORMALIZING FACTOR: C4 = 0.36908 STAGE 5 NORMALIZING FACTOR: C5 = 0.35624

Frequency Response

Buku Referensi Digital Signal Processing A System Design Approach By: David J Defatta Josepth G Lucas William S Hodkins Digital Signal Processing Principles, Algorithms & Application By: John G Proakis Dimitris G Monolokis

Correlation

Correlation is a maximum when two signals are similar in shape, and are in phase (or 'unshifted' with respect to each other).

Three different types of signal

Autocorrelation

Cross correlation to identify a signal

Convolution

If one signal is symmetric, convolution and correlation are identical

Fourier Transforms

FIR

FIR design by the window

IIR

The Z Transform

Poles and Zeroes

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