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7 votes

Is there a linear filter whose step response is an S-curve?

Sums of harmonic cosines The Hann window is a sum of a rectangular function and a truncated cosine. As an impulse response it has the qualities you asked for: Figure 1. Hann window as impulse ...
Olli Niemitalo's user avatar
6 votes
Accepted

How to determine the step response given a transfer function?

The short answer is that the step response is the inverse Laplace Transform of $\frac{1}{s}G(s)$. Here are some hints that should help in being able to solve the problem. Since it is likely a ...
Dan Boschen's user avatar
  • 52.1k
6 votes
Accepted

Transfer function with blackbox modelling is too slow compared to real expectation

In your original code you defined the sampling interval to be $T_s=0.05$ (idd1 = iddata(ddout, ddin, 0.05);). Yet, according to the data file, the time step between ...
Matt L.'s user avatar
  • 90.4k
5 votes

Pade Approximation of dead time

As explained in Tendero's answer everything you've calculated is correct. Matlab is supposed to complain because the system with transfer function $$H(s)=1-sT\tag{1}$$ has (assuming causality) a ...
Matt L.'s user avatar
  • 90.4k
5 votes
Accepted

Pade Approximation of dead time

There is no misunderstanding at all. The Padé approximant you found is correct. The "problem" is that you chose $M$ and $N$ such that the transfer function you get to approximate the delay is ...
Tendero's user avatar
  • 5,020
5 votes

Which step response matches the system transfer function

Open loop gain at DC is -3dB or .707 and 0 degrees. We don’t know the forward gain but assuming it is the open loop gain, the closed loop gain would be $.707/(1+.707)= .4148$, matching the first plot. ...
Dan Boschen's user avatar
  • 52.1k
5 votes
Accepted

Which step response matches the system transfer function

The final value of the step response is the DC gain of the closed-loop transfer function, which is generally different from the open-loop DC gain. Assuming unity gain feedback, the feed-forward ...
Matt L.'s user avatar
  • 90.4k
4 votes
Accepted

Step response of a differentiating system

If your system is an ideal differentiator with input-output relation $$y(t)=\frac{dx(t)}{dt}\tag{1}$$ then its transfer function is $$H(s)=\frac{Y(s)}{X(s)}=s\tag{2}$$ From the equation in your ...
Matt L.'s user avatar
  • 90.4k
4 votes

how to find the inverse response of a system

Dan's answer -- to compute $H(s)$ as normal, and then compute $1/H(s)$ -- is equivalent to your suggestion of swapping the $x$ and $y$ (or doing it in one step by solving for $H_{yx}(s) = \frac{X(s)}{...
TimWescott's user avatar
  • 12.8k
4 votes
Accepted

How do I get a faster system response?

The transfer function is $H(s) = \frac{16.94s + 579.5}{s^2 + 507.2s + 1224}$ This transfer function has 2 poles, one slow pole at -2.4248 and a fast pole at -504.7752. The function has a slowish zero ...
Ben's user avatar
  • 3,777
4 votes
Accepted

Convert filtering source C-code into difference equation

This one is a little difficult to transcribe since it uses the same variable temp for two different purposes. Across calls it's your state variable but during the ...
Hilmar's user avatar
  • 45.4k
3 votes
Accepted

What is the step response curve of a second order low pass filter? And what if it is set for resonance?

I can help with some of your multiple questions. First, a cascade of n buffered RC low pass filters (LPFs), a so-called n-th order synchronous LPF, has the impulse response and step response shown in ...
Ed V's user avatar
  • 795
3 votes
Accepted

How can I convert a step response that is described by the sum of two exponents to an IIR filter analytically?

You can use the step-invariant transformation, which makes sure that the step response of the discrete-time system matches the step response of the continuous-time system at the sampling instants. I ...
Matt L.'s user avatar
  • 90.4k
3 votes
Accepted

Relating transfer functions with step responses

In the given example you have 3 types of systems: the ideal integrator (D) with a step response that grows infinitely (fig. 1); that's the obvious one, as you've found out by yourself. underdamped ...
Matt L.'s user avatar
  • 90.4k
3 votes

Impulse response of a certain system

Let me provide a method, applied only for finding the impulse response $h(t)$ of an LTI system characterised by an LCCDE of the form $ \sum_{k=0}^{N}{ a_k {{d^k y(t)}\over {dt^k}}} = \sum_{k=0}^{M}{ ...
Fat32's user avatar
  • 28.3k
3 votes

What is a "jump response" of a filter?

It's a bad translation of step response, i.e., the filter's response to a unit step $u[n]$ at the input. Note that the step response is the convolution of the unit step with the filter's impulse ...
Matt L.'s user avatar
  • 90.4k
3 votes
Accepted

how to find the inverse response of a system

A general approach would be to take the Laplace Transform of the equation and put it in form of a transfer function: $$H(s) = \frac{Y(s)}{X(s)}$$ And then invert that and solve for the unit step ...
Dan Boschen's user avatar
  • 52.1k
3 votes
Accepted

Confusion regarding stability & step response?

An ideal integrator is not BIBO-stable, i.e., there are bounded input signals which result in an unbounded output. A step at the input is such a signal. Clearly, changing the sign of the transfer ...
Matt L.'s user avatar
  • 90.4k
2 votes
Accepted

Find transfer function from root locus and step response diagram?

The transfer function is $$H(s)=\frac{K(s - 4)(s + 5)}{(s + 3)(s + 6)(s + 10)}=\frac{K(s^2 + s - 20)}{s^3 + 19s^2 + 108s + 180}$$ So we need to find $K$. The LT of input step is $\frac{3}{s}$. ...
msm's user avatar
  • 4,295
2 votes

When input data into a low pass filter, are the first several data unusable?

You have to judge yourself if for your purposes you need to get rid of the first few output values. The phenomenon you observe is determined by two factors. The first is the delay of the filter (which ...
Matt L.'s user avatar
  • 90.4k
2 votes
Accepted

How to get Step Response from an Impulse Response in Simulink?

Your system H(s) is continuous $$ H(s) = \frac{s}{s+1} $$ Using a discrete impulse does not make a lot of sense. I suspect Simulink added a "zero-order hold" or ZOH block between your discrete ...
Ben's user avatar
  • 3,777
2 votes

How can i derive step response in terms of impulse response from the convolution sum?

In an LTI system, any linear operation on inputs, is directly imposed on the outputs, that is, if an LTI system responses to $\delta[n]$ as $h[n]$, then it responses to $u[n]=\sum_{k=-\infty}^{n}\...
Mostafa Ayaz's user avatar
2 votes

What is meant by "information encoded in time domain"?

The simplest (imho) explanation is this. Consider a time-domain signal which has narrow pulses or sudden jumps in value or on/off switches at certain (unknown!) time instants. Such a signal is said to ...
Fat32's user avatar
  • 28.3k
2 votes
Accepted

Root Locus, Transfer Functions and Unit Step Response?

The closed loop poles are the roots of the polynomial $$D(s)=s^2+2s+2+K\tag{1}$$ and, according to the root locus plot, they are $s_{1,2}=-1\pm 2j$. Consequently, we get $$2+K=|1+2j|^2=5\quad\...
Matt L.'s user avatar
  • 90.4k
2 votes
Accepted

Step response of bandpass fitler

The step response of your BPF has a fast decay, so you may eliminate it by setting the filter states. Have a look at the difference equation of your biquad BPF: $$ y[n] = 0.0377 x[n] + 0 x[n-1] - 0....
ZR Han's user avatar
  • 3,248
2 votes

How to plot step response of a system with more zeros than poles(Without changing original transfer function)

The transfer function you use is the one of an ideal differentiator, not of a practical one. So your system has a pole at infinity and the system is unstable. That's why Matlab can't plot the step ...
Matt L.'s user avatar
  • 90.4k
2 votes

What is the intuitive interpretation of the transfer function of this system?

but I also have a damper dissipating energy, which I don't see in my transfer function So, this is a fun one. You have a damper that dissipates energy when the external force is applied. However, ...
TimWescott's user avatar
  • 12.8k
2 votes

Convert filtering source C-code into difference equation

You got it! Except it's a recursive exponential moving average filter with $\alpha = 2^{-a}$ The difference equation is indeed: $$y[n] = \alpha x[n] + (1-\alpha)y[n-1]$$ $\mathcal{Z}$-transform to get:...
Jdip's user avatar
  • 6,265
2 votes
Accepted

Convolution of step function with exponentials

You got yourself into trouble by making things more complicated than they need be. First of all, note that $$(h\ast u)(t)=[(h_1+h_2)\ast u](t)=(h_1\ast u)(t)+(h_2\ast u)(t)$$ where $u(t)$ denotes the ...
Matt L.'s user avatar
  • 90.4k
2 votes
Accepted

Finding the impulse response of an c.t LTI system through the step response

Since the system is LTI, the input-output relationship is given by the convolution integral. Hence, for any signal $x(t)$, the output is given by $$ y(t) = (x*h)(t) = \int_{-\infty}^{+\infty}x(t-\tau)...
AHT's user avatar
  • 379

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