# Questions tagged [transfer-function]

Transfer function is a mathematical representation of relationship between input and output (signal) of a linear, time-invariant system.

512 questions
Filter by
Sorted by
Tagged with
5k views

### Are there alternatives to the bilinear transform?

When designing a digital filter based on an analog filter we usually use the bilinear transform. To approximate a discrete transfer function $D_a(z)$ from analog (continuous) transfer function $A(s)$ ...
• 5,216
35k views

### How poles are related to frequency response

I have recently fallen into fallacy, considering pole s=1 as there is infinite response at frequency 1. Yet, response was only 1. Now, can you derive the frequency response, given the poles? ...
• 1
2k views

4k views

### Digital filter coefficients from low-pass to high-pass

Given I have coefficients a0, a1, a2, b1, and b2, defining the difference equation for a digital filter as: ...
• 201
20k views

### Why more poles than zeroes?

I read that an "improper system" "has more zeros than poles; it is not causal, cannot be implemented, has a strictly proper inverse and has infinite high-frequency gain." Does causality fail due to ...
• 1
1k views

### If the convolution of two signals is a unit impulse, what does this tell us?

I have two discrete-time LTI systems whose transfer functions satisfy $h_1[n] * h_2[n]= \delta[n]$. We also know that system 1 is causal and stable. Does $h_1[n] * h_2[n]= \delta[n]$ tell us anything ...
• 249
8k views

### What is the relationship between poles and system stability?

I see two notions that describe the relationship between poles and system stability. But they are not the same from my understanding The system is BIBO stable if and only if all the poles are in the ...
• 71
12k views

### What Is the Transfer Function of a Moving Average (FIR Filter)?

To make post-processing easier, I export scope measurements as CSV files, which are then post-processed (mostly in Microsoft Excel, which is not the best tool for the job, but it is all I have at my ...
• 271
6k views

### Do Causal Discrete-time systems have proper transfer functions?

In the case of continuous-time systems, if the system is causal, its Laplace transfer function is strictly proper (the degree of the numerator is less than the degree of the denominator). Is this ...
559 views

### Does instability make an otherwise LTI system nonlinear (or time-variant)?

I am spinning this question off from the question from johnny. Matt L. and I have had directly opposite conclusions to johnny's question. I want to decouple the question from issues of causality and ...
134 views

### Who first coined "Direct Form I" and "Direct Form II"?

I see "Direct Form I" and "Direct Form II" commonly in literature to refer to FIR / IIR implementation from the filter transfer function, and reference it myself, but where did ...
• 51.3k
348 views

### For a discrete LTI system, does "bounded memory" imply "rational transfer function?"

Every LTI system with a $\mathcal Z$-domain transfer function that is a rational function - aka a quotient of two polynomials in $z$ - can be implemented using a bounded amount of memory. Is the ...
17k views

### Why eigen values and poles of a system are equivalent?

In control systems engineering, the stability of a system (modeled in the form of Transfer Function) is determined by the poles of the system in the right or left hand sides. When the model is ...
• 163
4k views

### Digital filters with more zeros than poles

I am having trouble wrapping my head around digital filters with different orders of numerator and denominator. Let me know if any of these points is wrong: All (digital or analog) transfer ...
• 15.8k
1k views

### Basic Questions on Wiener Filtering

I read a lot about Wiener Filters (focusing on discrete time case). I understand the math, but I am quite disconnected from the real life assumptions behind using such a filter. Unfortunately ...
2k views

### Relationship between the Real and Imaginary parts of a LTI causal system

Prelude I am writing an elaborate text on the relationship between the real and imaginary parts of a LTI causal system and how stability, causality and analyticity imposes various constraints on its ...
• 85
335 views

### Alternative derivation for a Thiran filter

Following this reasoning (link on ee.se) I'm trying to derive the transfer function for a Thiran filter, but I get stuck. I know of the original paper, I just thought I'd go this way. This is what I'm ...
• 1,828