Hi,
The attached file shows a simple smooth fade (taken from Farnell's"Designing Sound"). He writes: "A good way to obtain a smooth fade is to convert messages to a signal with [sig~] and then low pass filter it with [lop~]. A cuttoff value of 1Hz will make a fade that smoothly adjust over 1 second."

I do not understand what's the logic behind this rule. In the patch, a value (0-1) is transformed into signal, which means 64 samples of the same value, which are sent as a single block into the cold inlet of [*~]. So what's the deal with frequency here? Can someone clarify?
Thanks a lot

http://www.pdpatchrepo.info/hurleur/figure_14.6.tiff

The logic is quite simple. A low pass filter filters out high frequencies. When you have a control signal spitting out 0s and then at some point it just shifts directly to 1 in the span of 2 samples it will generate high frequency signal. You can even test it by sending it straight to your speaker, when it goes from 0 to 1 back to 0 in the span of 3 samples you'll hear a high click. The lowpass filter attenuate this high frequency by averaging out the change over a longer period of time creating the desired smooth fade.

While I think the idea is correct, in that a lop~ is just averaging the input. In reality I don't think it is strictly true that it works in the same way as a line object.

I remember being told how lop~ reacts but I can't recall the exact explanation

It seems that lop~ only actually tends towards 1 and never reaches it, I think this has something to do with it being a filter. You can see in the attached patch that a setting of 1Hz doesn't equate to a ramp of 1000ms. The [lop~] is always slower than the [vline~].

When I timed it, the results were more like ~1800ms!

http://www.pdpatchrepo.info/hurleur/lop-vs-vline.pd

Hi Saturno & Jwif
Thanks for your replies.
I guess I don't understand the role of the [lop~] here because I don't understand why a jump in values (lets say from 0 to 1) in few samples creates frequencies to begin with. For me the stream coming out of the slider is just values running at 44100 Hz, which are intended to change the amplitude of an audio signal. Does a change in their values create a change in frequency?

It's like the impulse response of a filter.

Maybe this diagram helps: http://www.rowetel.com/images/fixed_point_iir_impulse.png

Putting an impulse into a filter will average it out according to the cutoff frequency.

Messages are not quantized to the samples, so they're kinda independent of the sample rate. Frank explains it well here - http://lists.puredata.info/pipermail/pd-list/2011-02/086607.html

Although this still does not answer your question relating to the [lop~]

Jwif: You're right, it doesn't work like [line~]. I think the idea Andy's trying to present it that with a lowpass filter you can create curved transitions instead of lines.

ymotion: The high frequency content can be a difficult concept to wrap one's head around at first. Basically, when you have a sudden jump between two samples (say from 0 to 1) you have what's called a discontinuity. Now, according to Fourier theory, signals can be defined as a sum of sinusoids at different frequencies. The only way to create a discontinuity is for there to be an infinite number of frequencies that happen to be perfectly in phase at that exact moment. So, every time you move the slider, [sig~] is making a sudden jump from the last value to the new one. The lowpass filter is getting rid of a lot of the high frequencies, which has the effect of smoothing it out.

I fairly recently was trying to make one of those smoothed-out sample-and-hold LFOs and discovered that [lop~] generates asymmetric curves: logarithmic going up and exponential going down. It definitely was not useful in that situation. I was looking more for an S-curve. Turns Bessel filters do this (they also slightly overshoot the target value and oscillate a little before settling--something to keep in mind). If you wanted to get a straight line between values, a moving average filter will do that. Basically what I'm saying here is, if you have a preferred curve in mind, try out different filters to find the closest one.

The attached patch should help to visualize the curves.

http://www.pdpatchrepo.info/hurleur/smoothsteps.mmb.pd

If you think of the shapes of a slow (low pitch) sine oscillation and a fast (high pitch) sine, the fast sine has steeper slopes. Now all signals can be recreated by sinewaves (fourier transform.) So any signal that has a fast change of value if you think in terms of frequencies has high frequencies in. Using a LP filter gets rid of the high frequencies and so smooths the signal out.

Jwif - the Xn are the values coming from the slider, and Yn are the frequency after a lop was applied?
Didn't understand a word from what Frank wrote...

dullard: Yeah, that probably is an easier way to think about it.

Thanks for describing it more succinctly than I could Maelstrom (edit: and dullard)

Thanks for the patch, very interesting to know about [lop~] being log going up and exp going down. It's similar to the curve you get for an rms average.

I was wondering how I could make S-curves, I'll have to check out Bessel filters (currently using vanilla though).

I was doing crossfading a few weeks ago and found using the cos~ function to create equal power curves pretty useful.

@ymotion said:

Jwif - the Xn are the values coming from the slider, and Yn are the frequency after a lop was applied?

Almost. Like you said, the Xn graph represents the slider going from 1 to 0 very quickly.

Yn is not showing the frequency but rather the change in sample values (from 1 to 0) over a longer period, this is the output of the [lop~]. How fast this occurs would be the frequency.

OK, It is complicated, but I think I got it now.
Maelstorm & dullard: thanks for the visual descriptions. It's easier for me to follow this way...

@Maelstorm said:

I fairly recently was trying to make one of those smoothed-out sample-and-hold LFOs and discovered that [lop~] generates asymmetric curves: logarithmic going up and exponential going down.

Well, it's actually exponential both ways, but it's always exponentially decaying toward the destination value. So going up it's an inverted exponential decay.

But if you're considering something like an amplitude envelope, you may want the rising portions to be an exponential decay (most analog envelope generators work this way, moving to the next stage at a preset threshold). A DX7 has a true exponentially increasing attack (since it's a linear function passed through an exponential lookup table), but it sounds strange and sort of unmusical, like a sound played in reverse.

As suggested in the tutorials, quartic envelopes are a nice compromise. The curves are exponential-like, but they reach the destination values in a finite amount of time.

Thanks for the clarification acreil

It'd be cool to have a nice list somewhere of different envelopes, how they can be made and what situations they're useful for.

@Jwif said:

@ymotion said:

Jwif - the Xn are the values coming from the slider, and Yn are the frequency after a lop was applied?

Almost. Like you said, the Xn graph represents the slider going from 1 to 0 very quickly.

Yn is not showing the frequency but rather the change in sample values (from 1 to 0) over a longer period, this is the output of the [lop~]. How fast this occurs would be the frequency.

just to make sure, the values drop immediately from 1 to 0.12, and then gradually from 0.12 to 0? This sudden drop from 1 to 0.12 does not produce any clicks?

Sorry, I just found that image on google to try and explain it, it's not the actual output of [lop~].

Check out Maelstrom's smoothsteps.mmb patch he linked, it shows a graph of the curve.

OK, thanks Jwif