That's correct, the operation I was asking involves a convolution and a product. I looked at it more myself and tried it out on a few functions, and I think this might not be possible?
To further clarify, I was wondering if the product of the convolution of x(f) and g(f) with z(f) is equal to...
Ok thanks mathman and chiro! That makes sense. I just wondered if the associative property still applied with three arbitrary functions, because in all the places I've looked so far there is only two functions and a scalar used for the associative property. I'll think about it a bit further but...
Hi,
I have a quick question about certain algebraic properties of convolution. If I have 3 functions x(f), y(f) and z(f), is the following true?
[x(f) . g(f)] * z(f) = [x(f) * z(f)].g(f)
I looked on Wikipedia but there's only a property like this if one of the terms is a scalar, so most...
Hi all, I am just trying to prove to myself the Fourier series representation of a periodic rectangular pulse train. The pulses have some period T, and each pulse has magnitude equal to 1 over a duration of T/4, and 0 the rest of the cycle.
Using trignometric Fourier series, I get the...
Hi guys,
I am just having a bit of difficulty figuring out how to do convolution of impulses. Suppose I have a function consisting of impulses located at -2ω0, 0, and +2ω0 (in frequency domain) with some arbitrary amplitude A. I want to convolve this function with another function consisting of...
Homework Statement
Hi, I have a basic MOS common-drain amplifier as described below:
- Drain connected to 5 V DC
- Gate connected to an AC source on top of a 3 V DC source
- Source connected to a 200 uA current source with a resistor R connected in parallel. The parallel connection goes...
If I have 2 cosine terms added together, how would I combine them into one cosine term?
Ex:
A) 3 cos(2t)
B) cos(2t - pi/2)
Thanks
PS. I don't think the sum to product formulas work, I'm wondering how to combine them into a single cosine term?
Homework Statement
Use the node voltage method to find v in the circuit shown.
(picture of circuit attached)
Homework Equations
The Attempt at a Solution
v1 + (v1 - v2)/8 = 4.5
(v2 - v1)/8 + (v2)/12 + (v2 - 30)/4 = 0
Solving for v1 and v2 I get:
v1 = 6 V
v2 = 18 V
I...
Homework Statement
When finding the Thevenin resistance for a circuit, there is a method involving applying either a test voltage source or a test current source at the terminals a and b. My teacher didn't really go into this in very much detail so I was wondering if you can specify any value...
Thanks tiny-tim for the reply, but I'm a little confused on what you said on how to figure out which is the inertial frame. How do you know in which one the clocks go slower?
Homework Statement
1) You are gliding over Earth's surface at a high speed, carrying your high-precision clock. At points X and Y on the ground are similar clocks, synchronized in the ground frame of reference. As you pass over clock X, it and your clock both read 0. (a) According to you, do...
Homework Statement
For the matrix A =
-1, 5
-2, -3
I found the eigenvalues to be -2 + 3i and -2 - 3i.
Now I need some help to find the eigenvectors corresponding to each.
Homework Equations
The Attempt at a Solution
For r = -2 + 3i, I plugged that into the (A - Ir) matrix...
Homework Statement
Use Euler's formula to write the given expression in the form a + ib:
e^(2-(pi/2)i)
Homework Equations
Euler's formula: e^(it) = cos(t) + i*sin(t)
The Attempt at a Solution
I'm not sure how to get started on this one... am I supposed to get the expression into...
Homework Statement
Find the general solution of the given differential equation:
y'' + 9y = (t^2)(e^3t) + 6
Homework Equations
The Attempt at a Solution
I want to first find a particular solution using the method of undetermined coefficients, but I'm not sure what I should...
Homework Statement
Let y = y1(t) be a solution of
y' + p(t)y = 0, (i)
and let y = y2(t) be a solution of
y' + p(t)y = g(t). (ii)
Show that y = y1(t) + y2(t) is also a solution of Eq. (ii)
Homework Equations
The Attempt at a Solution
I'm not really sure how to start...