LAPORAN PROYEK SINYAL DAN SISTEM

ELLIPTIC FILTER

KELOMPOK 22

RIRY RIZKY ARUMDINA (0906632695)

YESSICA RATRI WIGUNA (0906632751)

ZESYARA MELATI AUZRIANI G. (0906512753)

BAB I

TEORI

Sebuah filter eliptik (juga dikenal sebagai Cauer filter, dinamai

Wilhelm Cauer ) adalah pemrosesan sinyal filter dengan menyamakan

kedudukan equiripple baik di passband maupun stopband. Jumlah

equiripple dalam band masing-masing secara independen disesuaikan,

dan tidak ada filter sama lain agar dapat memiliki transisi lebih cepat

dalam keuntungan antara passband dan stopband , nilai-nilai tertentu

ripple apakah yang disamakan atau tidak.

Keuntungan dari lowpass filter eliptik sebagai fungsi frekuensi

sudut ω diberikan oleh:

dimana n R adalah n-order ke fungsi rasional eliptik (kadang-

kadang dikenal sebagai fungsi rasional Chebyshev) dan

ω 0 adalah frekuensi cutoff

ε adalah faktor ripple

ξ adalah faktor selektivitas

Nilai dari faktor ripple menentukan ripple passband, sedangkan

kombinasi faktor ripple dan faktor selektifitas menentukan ripple

stopband.

Dalam passband, fungsi rasional eliptik bervariasi antara nol dan

kesatuan. Keuntungan yang demikian akan bervariasi antara 1 dan

.

Dalam stopband, fungsi rasional eliptik bervariasi antara tak terhingga

dan faktor diskriminasi n L yang didefinisikan sebagai:

Keuntungan dari stopband tersebut sehingga akan bervariasi antara 0

dan

Paramete

r

Deskripsi

Wp Passband corner frequency (Wp), cut off frekuensi, adalah

sebuah skalar atau vektor 2 element dengan nilai antara 0

dan 1, dimana 1 sesuai untuk Nyquist normalized frekuensi,

π radians per sample

Ws Stopband corner frekuensi (Ws), adalah skalar atau vektor 2

elemen dengan nilai antara 0 dan 1, dimana 1 sesuai untuk

Nyquist normalized frekuensi

Rp Passband Ripple, dalam decibel. Rp adalah nilai maksimum

yang diperboleh pada pasband loss, dalam decibel

Rs Stopband attenuation, dalam decibel. Rs adalah jumlah

decibel pada stopband yang terattenuasi dengan melihat ke

passband response

Berikut adalah tipe filter dan spesifikasi/syarat pada elliptic filter

Tipe

Filter

Stopband dan Passband

Condition

Stopband Passband

Lowpass Wp < Wn, keduanya skalar (Wn , 1) (0 , Wp)

Highpass Wp > Wn, keduanya skalar (0 , Wn) (Wp ,1)

Bandpass Wn (1) < Wp (1) < Wp (2) <

Wn(2)

(0,Wn(1))

dan

(Wn(2),1)

(Wp(1),

Wp(2))

Bandstop Wp (1) < Wn (1) < Wn (2) <

Wp (2)

(0, Wp(1))

dan

(Wp(2),1)

(Wn(1),

Wn(2))

Pada filter elliptic ini diperlukan input data berupa orde filternya

lalu ripple pada passband lalu stopband attenuation , passband

frequency. Itu merupakan input utama untuk tipe filter lowpass dan

highpass. Untuk filter tipe bandpass dan bansstop maka diperlukan

stopband frequency karena seperti yang kita ketahui bahwa pada tipe

tersebut frekuensi cut off nya ada dua. Kemudian pada semua jenis

tersebut dibutuhkan input frekuensi sampling yang nantinya digunakan

untuk mendapatkan normalisasi frekuensinya.

Bab II

PROGRAM

function varargout = coba(varargin)% COBA M-file for coba.fig% COBA, by itself, creates a new COBA or raises the existing% singleton*.%% H = COBA returns the handle to a new COBA or the handle to% the existing singleton*.%% COBA('CALLBACK',hObject,eventData,handles,...) calls the local% function named CALLBACK in COBA.M with the given input arguments.%% COBA('Property','Value',...) creates a new COBA or raises the% existing singleton*. Starting from the left, property value pairs are% applied to the GUI before coba_OpeningFcn gets called. An% unrecognized property name or invalid value makes property application% stop. All inputs are passed to coba_OpeningFcn via varargin.%% *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one% instance to run (singleton)".%% See also: GUIDE, GUIDATA, GUIHANDLES % Edit the above text to modify the response to help coba % Last Modified by GUIDE v2.5 04-May-2011 07:23:05 % Begin initialization code - DO NOT EDITgui_Singleton = 1;gui_State = struct('gui_Name', mfilename, ... 'gui_Singleton', gui_Singleton, ... 'gui_OpeningFcn', @coba_OpeningFcn, ... 'gui_OutputFcn', @coba_OutputFcn, ... 'gui_LayoutFcn', [] , ...

'gui_Callback', []);if nargin && ischar(varargin{1}) gui_State.gui_Callback = str2func(varargin{1});end if nargout [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});else gui_mainfcn(gui_State, varargin{:});end% End initialization code - DO NOT EDIT % --- Executes just before coba is made visible.function coba_OpeningFcn(hObject, eventdata, handles, varargin)% This function has no output args, see OutputFcn.% hObject handle to figure% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)% varargin command line arguments to coba (see VARARGIN) % Choose default command line output for cobahandles.output = hObject; % Update handles structureguidata(hObject, handles); % UIWAIT makes coba wait for user response (see UIRESUME)% uiwait(handles.figure1); % --- Outputs from this function are returned to the command line.function varargout = coba_OutputFcn(hObject, eventdata, handles) % varargout cell array for returning output args (see VARARGOUT);% hObject handle to figure% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA) % Get default command line output from handles structurevarargout{1} = handles.output; function edit1_Callback(hObject, eventdata, handles)

% hObject handle to edit1 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of edit1 as text% str2double(get(hObject,'String')) returns contents of edit1 as a doubleuser_string = get(hObject,'String'); function edit2_Callback(hObject, eventdata, handles)

% hObject handle to edit2 (see GCBO)

Untuk ambil data input pada bagian enter order

% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of edit2 as text% str2double(get(hObject,'String')) returns contents of edit2 as a double % --- Executes during object creation, after setting all properties.function edit2_CreateFcn(hObject, eventdata, handles)% hObject handle to edit2 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows.% See ISPC and COMPUTER.if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white');end function edit3_Callback(hObject, eventdata, handles)

% hObject handle to edit3 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of edit3 as text% str2double(get(hObject,'String')) returns contents of edit3 as a double % --- Executes during object creation, after setting all properties.function edit3_CreateFcn(hObject, eventdata, handles)% hObject handle to edit3 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows.% See ISPC and COMPUTER.if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white');end function edit4_Callback(hObject, eventdata, handles)

% hObject handle to edit4 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of edit4 as text% str2double(get(hObject,'String')) returns contents of edit4 as a double

Untuk ambil data input pada bagian enter ripple [dB]

Untuk ambil data input pada bagian enter stopband attenuation (dalam dB)

FUNGSI TRANSFER

% --- Executes during object creation, after setting all properties.function edit4_CreateFcn(hObject, eventdata, handles)% hObject handle to edit4 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows.% See ISPC and COMPUTER.if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white');end function edit5_Callback(hObject, eventdata, handles)

% hObject handle to edit5 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of edit5 as text% str2double(get(hObject,'String')) returns contents of edit5 as a double % --- Executes during object creation, after setting all properties.function edit5_CreateFcn(hObject, eventdata, handles)% hObject handle to edit5 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows.% See ISPC and COMPUTER.if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white');end % --- Executes on button press in pushbutton1.function pushbutton1_Callback(hObject, eventdata, handles)% hObject handle to pushbutton1 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA)select=get(handles.popupmenu1,'Value'); n =str2double(get(handles.edit2,'String'))Rp =str2double(get(handles.edit3,'String'))Rs =str2double(get(handles.edit4,'String')) if select == 2 Wp =str2double(get(handles.edit5,'String'))[z,p,k] = ellip(n,Rp,Rs,Wp,'low');[sos,g] = zp2sos (z,p,k);Hd= dfilt.df2tsos (sos,g);

h = fvtool (Hd);set (h, 'analysis', 'freq')

Untuk ambil data program ke GUI pada pilihan tipe filter

Untuk ambil data input pada bagian enter passband edge frequency[0 -1]

Pilihan LOWPASS

Pilihan HIGHPASS

Pemunculan grafik

FUNGSI TRANSFER

FUNGSI TRANSFER

FUNGSI TRANSFER

Pemunculan grafik

elseif select == 3 Wp =str2double(get(handles.edit5,'String')) [z,p,k] = ellip(n,Rp,Rs,Wp,'high');

[sos,g] = zp2sos (z,p,k); Hd= dfilt.df2tsos (sos,g);

h = fvtool (Hd);set (h, 'analysis', 'freq') elseif select == 5 Wn1 =str2double(get(handles.edit5,'String')) Wn2 =str2double(get(handles.edit6,'String')) Wn=[Wn1 Wn2];ftype= 'bandpass'; [z,p,k]=ellip(n, Rp, Rs, Wn, ftype);[sos,g]=zp2sos(z,p,k);Hd=dfilt.df2sos(sos,g); h = fvtool (Hd);set (h, 'analysis', 'freq') elseif select == 4 Wn1 =str2double(get(handles.edit5,'String')) Wn2 =str2double(get(handles.edit6,'String')) Wn=[Wn1 Wn2];ftype= 'stop'; [z,p,k]=ellip(n, Rp, Rs, Wn, ftype);[sos,g]=zp2sos(z,p,k);Hd=dfilt.df2sos(sos,g); h = fvtool (Hd);set (h, 'analysis', 'freq') end function edit6_Callback(hObject, eventdata, handles)

% hObject handle to edit6 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA) % Hints: get(hObject,'String') returns contents of edit6 as text% str2double(get(hObject,'String')) returns contents of edit6 as a double % --- Executes during object creation, after setting all properties.function edit6_CreateFcn(hObject, eventdata, handles)% hObject handle to edit6 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles empty - handles not created until after all CreateFcns called % Hint: edit controls usually have a white background on Windows.

Untuk ambil data input pada bagian enter stopband edge frequency[0 -1]

Pilihan BANDSTOP

Pilihan BANDPASS

Pemunculan grafik

Pemunculan grafik

% See ISPC and COMPUTER.if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white');end % --- Executes on selection change in popupmenu1.function popupmenu1_Callback(hObject, eventdata, handles)

% hObject handle to popupmenu1 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA) % Hints: contents = get(hObject,'String') returns popupmenu1 contents as cell array% contents{get(hObject,'Value')} returns selected item from popupmenu1 % --- Executes during object creation, after setting all properties. % --- If Enable == 'on', executes on mouse press in 5 pixel border.% --- Otherwise, executes on mouse press in 5 pixel border or over edit2.function edit2_ButtonDownFcn(hObject, eventdata, handles)% hObject handle to edit2 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles structure with handles and user data (see GUIDATA) sel_typ = get(gcbf,'SelectionType') if sel_type == 'normal' set(hObject,'String','') end % --- Executes during object creation, after setting all properties.function popupmenu1_CreateFcn(hObject, eventdata, handles)% hObject handle to popupmenu1 (see GCBO)% eventdata reserved - to be defined in a future version of MATLAB% handles empty - handles not created until after all CreateFcns called % Hint: popupmenu controls usually have a white background on Windows.% See ISPC and COMPUTER.if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white');end

Memanggil pilihan select filter type yang didalamnya terdapat 4 tipe

Untuk LOWPASS FILTER

Untuk HIGHPASS FILTER

Untuk BANDPASS FILTER

Untuk BANDSTOP FILTER

BAB III

PENUTUP

Demikianlah laporan ini, penulis berharap laporan ini dapat

menjelaskan apa saja yang tertera pada program filter elliptic. Penulis

juga memohon maaf apabila ada kesalahan-kesalahan yang terjadi baik

itu sengaja maupun tidak sengaja. Atas segala dukungannya penulis

mengucapkan terima kasih. Dalam program ini terdapat beberapa

kekurangan dan kelebihan. Berikut penjelasan kelebihan dan kekurangan

program.

KEKURANGAN

1. Program ini terkadang error dan tidak mau menampilkan grafik ke

user apabila menggunakan file copy dari program asli.

2. Program ini tidak menyediakan menu menampilkan fungsi transfer

(H(jω)), walaupun dalam program ini memanfaatkan fungsi transfer

hingga terbentuk grafik.

KELEBIHAN

Program ini sudah memanfaatkan GUI sehingga lebih memudahkan

user.