Pole-zeros of a real-valued causal FIR system The Next CEO of Stack OverflowPoles and Zerospole/zero locations for real and imaginary signalIdentifying the magnitude and impulse response from pole zero plot quicklySystem characterization given pole-zero mappingWhat's the Q of a pole at the origin of the s-plane?How to find system function, H(z) in the z-domain, given zero-pole plot of the system?Conjugate Pole PairsQuestion about poles and zeros in AR filterDetermine poles and zeros of a specific filter designHow to determine if a filter is bandpass/stopband from its pole-zero diagram in z-domain
Several mode to write the symbol of a vector
How to avoid supervisors with prejudiced views?
Is there a difference between "Fahrstuhl" and "Aufzug"
Is there an analogue of projective spaces for proper schemes?
Should I tutor a student who I know has cheated on their homework?
Bold, vivid family
WOW air has ceased operation, can I get my tickets refunded?
Sending manuscript to multiple publishers
Won the lottery - how do I keep the money?
How to transpose the 1st and -1th levels of arbitrarily nested array?
Received an invoice from my ex-employer billing me for training; how to handle?
Can we say or write : "No, it'sn't"?
How to count occurrences of text in a file?
What expression will give age in years in QGIS?
Is HostGator storing my password in plaintext?
Why do we use the plural of movies in this phrase "We went to the movies last night."?
Interfacing a button to MCU (and PC) with 50m long cable
What exact does MIB represent in SNMP? How is it different from OID?
Is it professional to write unrelated content in an almost-empty email?
Contours of a clandestine nature
How does the mv command work with external drives?
Skipping indices in a product
Why does standard notation not preserve intervals (visually)
How did people program for Consoles with multiple CPUs?
Pole-zeros of a real-valued causal FIR system
The Next CEO of Stack OverflowPoles and Zerospole/zero locations for real and imaginary signalIdentifying the magnitude and impulse response from pole zero plot quicklySystem characterization given pole-zero mappingWhat's the Q of a pole at the origin of the s-plane?How to find system function, H(z) in the z-domain, given zero-pole plot of the system?Conjugate Pole PairsQuestion about poles and zeros in AR filterDetermine poles and zeros of a specific filter designHow to determine if a filter is bandpass/stopband from its pole-zero diagram in z-domain
$begingroup$
Could someone please help me with the following question?
Below is the magnitude response of a real-valued causal linear phase FIR system of order N = 6. Determine the location of poles and zeros.
I know that for FIR systems all the poles are located at the origin, so we have a pole of order six at the origin. Also from the given diagram, I can say that we have a zero at 0.3pi and one at 0.8pi (both on the unit circle). Now since the system is real-valued, location of poles and zeros should be symmetric w.r.t. the real axis. But I don't know about the two other zeros?
Also, what about the pick in the diagram? Does it mean we have another pole?
fir poles-zeros
$endgroup$
add a comment |
$begingroup$
Could someone please help me with the following question?
Below is the magnitude response of a real-valued causal linear phase FIR system of order N = 6. Determine the location of poles and zeros.
I know that for FIR systems all the poles are located at the origin, so we have a pole of order six at the origin. Also from the given diagram, I can say that we have a zero at 0.3pi and one at 0.8pi (both on the unit circle). Now since the system is real-valued, location of poles and zeros should be symmetric w.r.t. the real axis. But I don't know about the two other zeros?
Also, what about the pick in the diagram? Does it mean we have another pole?
fir poles-zeros
$endgroup$
add a comment |
$begingroup$
Could someone please help me with the following question?
Below is the magnitude response of a real-valued causal linear phase FIR system of order N = 6. Determine the location of poles and zeros.
I know that for FIR systems all the poles are located at the origin, so we have a pole of order six at the origin. Also from the given diagram, I can say that we have a zero at 0.3pi and one at 0.8pi (both on the unit circle). Now since the system is real-valued, location of poles and zeros should be symmetric w.r.t. the real axis. But I don't know about the two other zeros?
Also, what about the pick in the diagram? Does it mean we have another pole?
fir poles-zeros
$endgroup$
Could someone please help me with the following question?
Below is the magnitude response of a real-valued causal linear phase FIR system of order N = 6. Determine the location of poles and zeros.
I know that for FIR systems all the poles are located at the origin, so we have a pole of order six at the origin. Also from the given diagram, I can say that we have a zero at 0.3pi and one at 0.8pi (both on the unit circle). Now since the system is real-valued, location of poles and zeros should be symmetric w.r.t. the real axis. But I don't know about the two other zeros?
Also, what about the pick in the diagram? Does it mean we have another pole?
fir poles-zeros
fir poles-zeros
asked 2 days ago
NioushaNiousha
1596
1596
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Note the difference between the zeros at $0.3 pi$ and at $0.8 pi$.
The first one is clearly a zero crossing, much like $abs(x)$ at $x=0$.
At $theta = 0.8 pi$, however, the curve is tangent to the horizontal axis, much like $x^2$ at $x=0$. So you have a doulbe zero here.
So your zeros are:
- 2 zeros at $z = e^pm j 0.3 pi$
- 2 double zeros at $z = e^pm j 0.8 pi$
$endgroup$
add a comment |
$begingroup$
Causality places the transfer-function poles at $z=0$, for a FIR filter.
A FIR filter need not necessarily be causal, in which case some or all of its poles reside at $z=infty$ (if not at $z=0$). In any of these cases, the poles play no role in shaping frequency response, since they remain equidistant from the unit circle.
(A value of $k$ in the range of $[-1, 1]$ can place conjugate pole pairs anywhere on the unit circle, where they are most effectual in shaping frequency response.)
$$beginaligned
fracz^2 +2kz + 1z^2 &mboximplies y_n=x_n + 2kx_n-1 + x_n-2 \
z^2 +2kz + 1 &mboximplies y_n=x_n+2 + 2kx_n+1 + x_n
endaligned$$
New contributor
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "295"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fdsp.stackexchange.com%2fquestions%2f56275%2fpole-zeros-of-a-real-valued-causal-fir-system%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Note the difference between the zeros at $0.3 pi$ and at $0.8 pi$.
The first one is clearly a zero crossing, much like $abs(x)$ at $x=0$.
At $theta = 0.8 pi$, however, the curve is tangent to the horizontal axis, much like $x^2$ at $x=0$. So you have a doulbe zero here.
So your zeros are:
- 2 zeros at $z = e^pm j 0.3 pi$
- 2 double zeros at $z = e^pm j 0.8 pi$
$endgroup$
add a comment |
$begingroup$
Note the difference between the zeros at $0.3 pi$ and at $0.8 pi$.
The first one is clearly a zero crossing, much like $abs(x)$ at $x=0$.
At $theta = 0.8 pi$, however, the curve is tangent to the horizontal axis, much like $x^2$ at $x=0$. So you have a doulbe zero here.
So your zeros are:
- 2 zeros at $z = e^pm j 0.3 pi$
- 2 double zeros at $z = e^pm j 0.8 pi$
$endgroup$
add a comment |
$begingroup$
Note the difference between the zeros at $0.3 pi$ and at $0.8 pi$.
The first one is clearly a zero crossing, much like $abs(x)$ at $x=0$.
At $theta = 0.8 pi$, however, the curve is tangent to the horizontal axis, much like $x^2$ at $x=0$. So you have a doulbe zero here.
So your zeros are:
- 2 zeros at $z = e^pm j 0.3 pi$
- 2 double zeros at $z = e^pm j 0.8 pi$
$endgroup$
Note the difference between the zeros at $0.3 pi$ and at $0.8 pi$.
The first one is clearly a zero crossing, much like $abs(x)$ at $x=0$.
At $theta = 0.8 pi$, however, the curve is tangent to the horizontal axis, much like $x^2$ at $x=0$. So you have a doulbe zero here.
So your zeros are:
- 2 zeros at $z = e^pm j 0.3 pi$
- 2 double zeros at $z = e^pm j 0.8 pi$
answered 2 days ago
JuanchoJuancho
3,8801315
3,8801315
add a comment |
add a comment |
$begingroup$
Causality places the transfer-function poles at $z=0$, for a FIR filter.
A FIR filter need not necessarily be causal, in which case some or all of its poles reside at $z=infty$ (if not at $z=0$). In any of these cases, the poles play no role in shaping frequency response, since they remain equidistant from the unit circle.
(A value of $k$ in the range of $[-1, 1]$ can place conjugate pole pairs anywhere on the unit circle, where they are most effectual in shaping frequency response.)
$$beginaligned
fracz^2 +2kz + 1z^2 &mboximplies y_n=x_n + 2kx_n-1 + x_n-2 \
z^2 +2kz + 1 &mboximplies y_n=x_n+2 + 2kx_n+1 + x_n
endaligned$$
New contributor
$endgroup$
add a comment |
$begingroup$
Causality places the transfer-function poles at $z=0$, for a FIR filter.
A FIR filter need not necessarily be causal, in which case some or all of its poles reside at $z=infty$ (if not at $z=0$). In any of these cases, the poles play no role in shaping frequency response, since they remain equidistant from the unit circle.
(A value of $k$ in the range of $[-1, 1]$ can place conjugate pole pairs anywhere on the unit circle, where they are most effectual in shaping frequency response.)
$$beginaligned
fracz^2 +2kz + 1z^2 &mboximplies y_n=x_n + 2kx_n-1 + x_n-2 \
z^2 +2kz + 1 &mboximplies y_n=x_n+2 + 2kx_n+1 + x_n
endaligned$$
New contributor
$endgroup$
add a comment |
$begingroup$
Causality places the transfer-function poles at $z=0$, for a FIR filter.
A FIR filter need not necessarily be causal, in which case some or all of its poles reside at $z=infty$ (if not at $z=0$). In any of these cases, the poles play no role in shaping frequency response, since they remain equidistant from the unit circle.
(A value of $k$ in the range of $[-1, 1]$ can place conjugate pole pairs anywhere on the unit circle, where they are most effectual in shaping frequency response.)
$$beginaligned
fracz^2 +2kz + 1z^2 &mboximplies y_n=x_n + 2kx_n-1 + x_n-2 \
z^2 +2kz + 1 &mboximplies y_n=x_n+2 + 2kx_n+1 + x_n
endaligned$$
New contributor
$endgroup$
Causality places the transfer-function poles at $z=0$, for a FIR filter.
A FIR filter need not necessarily be causal, in which case some or all of its poles reside at $z=infty$ (if not at $z=0$). In any of these cases, the poles play no role in shaping frequency response, since they remain equidistant from the unit circle.
(A value of $k$ in the range of $[-1, 1]$ can place conjugate pole pairs anywhere on the unit circle, where they are most effectual in shaping frequency response.)
$$beginaligned
fracz^2 +2kz + 1z^2 &mboximplies y_n=x_n + 2kx_n-1 + x_n-2 \
z^2 +2kz + 1 &mboximplies y_n=x_n+2 + 2kx_n+1 + x_n
endaligned$$
New contributor
New contributor
answered yesterday
KevinKevin
111
111
New contributor
New contributor
add a comment |
add a comment |
Thanks for contributing an answer to Signal Processing Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fdsp.stackexchange.com%2fquestions%2f56275%2fpole-zeros-of-a-real-valued-causal-fir-system%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown