impulse response units

hello forum.

convolution between the function x(t), with units of Volts, and h(t), the
system impulse response.
h(t) needs to have units of inverse time, in order for g(t), the output of
the convolution, to have units of Volts:

g(t)=summation {x(tau)*h(t-tau)}dtau

Correct?

2) If correct, take the signal exp(i*theta)
theta has units of radians.
If theta=(2*pi)*rand(N)-pi    (unif noise distribution btw -pi and pi)

The convolution between theta and the gaussian filter h(t) is:

theta_new= summation {theta(tau)* h(t-tau)}dtau

h(t) is normalized and has units of inverse time (due to the units of the
standard deviation).

Is it true that theta needs to be divided by delta_t before performing the
convolution? (delta_t being the sample spatial distance).

thanks
fisico30

On 4 Mar, 17:56, "fisico30" <marcoscipio...@gmail.com> wrote:
> hello forum.
>
> convolution between the function x(t), with units of Volts, and h(t), the
> system impulse response.
> h(t) needs to have units of inverse time, in order for g(t), the output of
> the convolution, to have units of Volts:
>
> g(t)=summation {x(tau)*h(t-tau)}dtau
>
> Correct?

How is this relevant to DSP?

> 2) If correct, take the signal exp(i*theta)
> theta has units of radians.
> If theta=(2*pi)*rand(N)-pi &#4294967295; &#4294967295;(unif noise distribution btw -pi and pi)
>
> The convolution between theta and the gaussian filter h(t) is:
>
> theta_new= summation {theta(tau)* h(t-tau)}dtau
>
> h(t) is normalized and has units of inverse time (due to the units of the
> standard deviation).
>
> Is it true that theta needs to be divided by delta_t before performing the
> convolution? (delta_t being the sample spatial distance).

It seems your question has more to do with mathematical
physics than DSP. Check out a newsgroup on physics or read
up on Green's functions. Or both.

Rune

>On 4 Mar, 17:56, "fisico30" <marcoscipio...@gmail.com> wrote:
>> hello forum.
>>
>> convolution between the function x(t), with units of Volts, and h(t),
the
>> system impulse response.
>> h(t) needs to have units of inverse time, in order for g(t), the output
o=
>f
>> the convolution, to have units of Volts:
>>
>> g(t)=3Dsummation {x(tau)*h(t-tau)}dtau
>>
>> Correct?
>
>How is this relevant to DSP?
>
>> 2) If correct, take the signal exp(i*theta)
>> theta has units of radians.
>> If theta=3D(2*pi)*rand(N)-pi =A0 =A0(unif noise distribution btw -pi
and =

Hello Rune,
sorry, I thought it would be a scaling issue that can give the wrong
computational results . I found that some people you might be right.......
thanks
>pi)
>>
>> The convolution between theta and the gaussian filter h(t) is:
>>
>> theta_new=3D summation {theta(tau)* h(t-tau)}dtau
>>
>> h(t) is normalized and has units of inverse time (due to the units of
the
>> standard deviation).
>>
>> Is it true that theta needs to be divided by delta_t before performing
th=
>e
>> convolution? (delta_t being the sample spatial distance).
>
>It seems your question has more to do with mathematical
>physics than DSP. Check out a newsgroup on physics or read
>up on Green's functions. Or both.
>
>Rune
>

On Mar 4, 1:30&#4294967295;pm, Rune Allnor <all...@tele.ntnu.no> wrote:
> On 4 Mar, 17:56, "fisico30" <marcoscipio...@gmail.com> wrote:
>
> > convolution between the function x(t), with units of Volts, and h(t), the
> > system impulse response.
> > h(t) needs to have units of inverse time, in order for g(t), the output of
> > the convolution, to have units of Volts:
>
> > g(t)=summation {x(tau)*h(t-tau)}dtau
>
> > Correct?

yes it is.  we've had both conversations and some little spats about
this in the past.  since a pair of wires is a possible LTI system that
maps an input voltage to an output, the Dirac impulse function has,
for its "dependent variable" reciprocal time also.  the dimension of
delta(x) is the reciprocal of the dimension of x.

> How is this relevant to DSP?

it's only relevant if you are expecting to sample continuous-time
signals to discrete-time  and/or reconstruct discrete-time signals to
continuous time and want to understand the net, overall transfer
function (or equivalently the impulse response).  nobody doing DSP
ever considers about such issues.

> > 2) If correct, take the signal exp(i*theta)
> > theta has units of radians.

measuring angle in radians is actually both unitless *and*
dimensionless.  it's arc length over radial arm length.  just a
number.  however, measuring angle in degrees is not unitless, but it
is still dimensionless.

> > If theta=(2*pi)*rand(N)-pi &#4294967295; &#4294967295;(uniform noise distribution btw -pi and pi)
> >
> > The convolution between theta and the gaussian filter h(t) is:
> >
> > theta_new= summation {theta(tau)* h(t-tau)}dtau
> >
> > h(t) is normalized and has units of inverse time (due to the units of the
> > standard deviation).
> >
> > Is it true that theta needs to be divided by delta_t before performing the
> > convolution? (delta_t being the sample spatial distance).

i think you need to be a little more clear with the question.  as best
as i can tell from what you have said so far is if theta_new and theta
(tau) share the same dimension (which appears to be the "dimension of
unity" a.k.a. "dimensionless"), then h(t) must be the reciprocal
dimension of tau (because the dtau has the dimension of tau) and no
other division by the dimension of tau is necessary (or correct).

r b-j