Oversampling using Cheby2 IIR FIlter.

Bernhard Holzmayer <Holzmayer.Bernhard@deadspam.com> wrote:

|4) Since the inserted samples are not perfectly correct, 
|   they'll introduce high frequency content which is undesirable, 
|   if you want to downsample afterwards.
|   If the target sampling rate of the following downsampling is 48.51kS/s
|   (factor 1.1), you'll have to make sure that the high-frequency stream 
|   has no frequencies higher than 24.255kHz.

Shouldn't you filter everything above 22.05 kHz?  Anything above that
frequency is noise from the upsampling.

(If you said this later, i appologize.  I didn't follow all of it.)

Phil

pgx@pgrahams.com wrote:

> Bernhard Holzmayer <Holzmayer.Bernhard@deadspam.com> wrote:
> 
> |4) Since the inserted samples are not perfectly correct,
> |   they'll introduce high frequency content which is undesirable,
> |   if you want to downsample afterwards.
> |   If the target sampling rate of the following downsampling is 48.51kS/s
> |   (factor 1.1), you'll have to make sure that the high-frequency stream
> |   has no frequencies higher than 24.255kHz.
> 
> Shouldn't you filter everything above 22.05 kHz?  Anything above that
> frequency is noise from the upsampling.
> 
> (If you said this later, i appologize.  I didn't follow all of it.)
Yes, I did.
> 
> Phil

Nevertheless: if this is necessary, depends on the samples which are
introduced. 
Which distortions would you expect between 22.05kHz and 24.255kHz, if
zero-padding were applied? 

The following process, however, doesn't require to remove the range between
22.05kHz and 24.255kHz: both sample rates which are used in the following
process, can handle this range without aliasing effects.
Bernhard

Bernhard Holzmayer <Holzmayer.Bernhard@deadspam.com> wrote:

|pgx@pgrahams.com wrote:
|
|> Bernhard Holzmayer <Holzmayer.Bernhard@deadspam.com> wrote:
|> 
|> |4) Since the inserted samples are not perfectly correct,
|> |   they'll introduce high frequency content which is undesirable,
|> |   if you want to downsample afterwards.
|> |   If the target sampling rate of the following downsampling is 48.51kS/s
|> |   (factor 1.1), you'll have to make sure that the high-frequency stream
|> |   has no frequencies higher than 24.255kHz.
|> 
|> Shouldn't you filter everything above 22.05 kHz?  Anything above that
|> frequency is noise from the upsampling.
|> 
|> (If you said this later, i appologize.  I didn't follow all of it.)
|Yes, I did.
|> 
|> Phil
|
|Nevertheless: if this is necessary, depends on the samples which are
|introduced. 
|Which distortions would you expect between 22.05kHz and 24.255kHz, if
|zero-padding were applied? 

The same distortions that produce frequencies above 24.255kHz.

If you should filter before downsampling, shouldn't you just filter
from 22.5kHz, since there is no usefull data at higher frequencies.

Phil

pgx@pgrahams.com wrote:

> Bernhard Holzmayer <Holzmayer.Bernhard@deadspam.com> wrote:
> 
> |pgx@pgrahams.com wrote:
> |
> |> Bernhard Holzmayer <Holzmayer.Bernhard@deadspam.com> wrote:
> |> 
> |> |4) Since the inserted samples are not perfectly correct,
> |> |   they'll introduce high frequency content which is undesirable,
> |> |   if you want to downsample afterwards.
> |> |   If the target sampling rate of the following downsampling is
> |> |   48.51kS/s (factor 1.1), you'll have to make sure that the
> |> |   high-frequency stream has no frequencies higher than 24.255kHz.
> |> 
> |> Shouldn't you filter everything above 22.05 kHz?  Anything above that
> |> frequency is noise from the upsampling.
> |> 
> |> (If you said this later, i appologize.  I didn't follow all of it.)
> |Yes, I did.
> |> 
> |> Phil
> |
> |Nevertheless: if this is necessary, depends on the samples which are
> |introduced.
> |Which distortions would you expect between 22.05kHz and 24.255kHz, if
> |zero-padding were applied?
> 
> The same distortions that produce frequencies above 24.255kHz.

I'd expect that zero-padding wouldn't introduce any in this range.
Can you explain this?

> 
> If you should filter before downsampling, shouldn't you just filter
> from 22.5kHz, since there is no usefull data at higher frequencies.

This is certainly true, in a practical sense.
However, it's of great advantage if I can rely on this region to be free of
parasitic signals. A filter with passband up to 22.05kHz and stopband from
24.255kHz would suffice, which is a very convenient one.
In the other case, if signals in this range have to be suppressed, this will
heavily influence the filter requirements: a very steep filter (high order)
would be necessary, and even then, it would be impossible to achieve
perfect suppression of the components beyond the 22.05kHz region while
conserving the complete passband region up to this frequency.
Bernhard