> Hello everyone,
>
> I am trying to introduce myself to DSP through the free book at
> (www.dspguide.com) on the Internet.
>
> I was studying the chapter on linear systems and it mentions that
> multiplying 2 signals together is not a linear operation. It gives the
> example that when you multiply 2 sinusoids of different frequencies,
> the result is clearly not a sinusoid.
>
> My question is how is that the test for the linearity of the system?
> Why should the multiplication of 2 sinusoids in a linear system
> produce another sinusoid?
>
> I hope I am expressing my query clearly enough... Would really
> appreciate if someone can help me clarify this doubt...
>
> Thanks,
> ...

> A definitiion and test for a linear system can be found here:
>
> http://en.wikipedia.org/wiki/Linear_system
>
> A system that multiplies two inputs fails the test.

>Hello everyone,
>
>I am trying to introduce myself to DSP through the free book at
>(www.dspguide.com) on the Internet.
>
>I was studying the chapter on linear systems and it mentions that
>multiplying 2 signals together is not a linear operation. It gives the
>example that when you multiply 2 sinusoids of different frequencies,
>the result is clearly not a sinusoid.
>
>My question is how is that the test for the linearity of the system?
>Why should the multiplication of 2 sinusoids in a linear system
>produce another sinusoid?

>>A definitiion and test for a linear system can be found here:
>>
>>http://en.wikipedia.org/wiki/Linear_system
>>
>>A system that multiplies two inputs fails the test.

>
>
> I looked at this page but am still unable to understand how and where
> it fails the test. Mathematics is not my strong point (though I am
> working on it every day!). Is it possible that you can explain a bit
> as to what constraints are violated?
>
> Thanks,
> Anja
>

> Hello everyone,
>
> I am trying to introduce myself to DSP through the free book at
> (www.dspguide.com) on the Internet.
>
> I was studying the chapter on linear systems and it mentions that
> multiplying 2 signals together is not a linear operation. It gives the
> example that when you multiply 2 sinusoids of different frequencies,
> the result is clearly not a sinusoid.

> On 6 Okt, 15:45, Anja googlemail.com> wrote:
>

>> Hello everyone,

>

>> I am trying to introduce myself to DSP through the free book at
>> (www.dspguide.com) on the Internet.

>

>> I was studying the chapter on linear systems and it mentions that
>> multiplying 2 signals together is not a linear operation. It gives the
>> example that when you multiply 2 sinusoids of different frequencies,
>> the result is clearly not a sinusoid.

>
> The linear system model is useful because it leaves you
> with a choise: Either express the input signal as one
> "complicated" signal, and apply the system function
> on this one signal. Or you can express the input as a
> sum of "simple" signals, where you apply the system function
> on each of these, and synthesize the total output signal
> as the sum of "simple" outputs. ...

> Hello everyone,
>
> I am trying to introduce myself to DSP through the free book at
> (www.dspguide.com) on the Internet.
>
> I was studying the chapter on linear systems and it mentions that
> multiplying 2 signals together is not a linear operation. It gives the
> example that when you multiply 2 sinusoids of different frequencies,
> the result is clearly not a sinusoid.
>
> My question is how is that the test for the linearity of the system?

>
> Multiplication with a fixed signal is a linear operation. A
> "system" (*) H is linear iff
>
> H(a x1 + b x2) = a H(x1) + b H(x2)
>
> for all a numbers a and b and all signals x1 and x2 (just showing the
> above condition to be true for a specific pair of signals will not
> do). Note that the system H takes one signal as an argument: H = H(x).
> Now what if H multplies its argument by sin(w t)?. You get
>
> H(a x1(t) + b x2(t))
> = sin(w t)(a x1(t)+b x2(t))
> = a sin(w t) x1(t) + b sin(w t) x2(t)
> = a H(x1(t)) + b H(x2(t)),
>
> so clearly H is a linear system. Systems can be generalized to more
> than one input or output. In this case you still write
>
> y = H(x), ...