FPGA Central

Dear all,

I am studying 2D DCT for an image. The 2D DCT can be summarized as computing
Y=T*X*T', where X is the input matrix, T is the 2D DCT basis matrix, Y is
the output.

X is integer 0-255. T is real-valued, 0 - 1.

In order to convert real-valued T to integers, I multiply T with 256(left
shift), and round it to integer, and use these new integer values in my
computing.

Now Y will be larger than its correct value by a factor of 256*256, so I
will divide it by 65536(right shift the result by 16 bits to get correct
result).

My question is, is my approach correct?

How many bits I need to allocate for internal matrix computation and the
output?

Is there any better approach to save some datawidth?

In general, are there any resources to study for dealing with
real-to-integer conversion?

Thanks a lot,

-Walala

Hi Vic,

> by prepared T you convert to int as T'=(int)(T+0.5).

T is a matrix with element in [0, 1]... so do you mean T'=round(T*2^b),
where 2^b is a scaling factor? But it is unclear to me how to choose this
scaling factor optimally?

> Y1=(T*X+1)>>1.

The above expression is quite unfamiliar to me... why +1 then >>1?

> Y=Y1*T will have 15 bit exactitude, scaler 128 in mind.

If you choose b=7, scaling 128, then the final result will be scaling
128*128=16384(14 bits), right?

Sorry I may need more help on this, can you explain to me a little more in
details?

Thanks a lot,

-Walala

Hi Walala,
i answered fastly but with errors as see now.
> > by prepared T you convert to int as T'=(int)(T+0.5).
sorry my negligance: T'=(int)(T>>8+0.5) .

> > Y1=(T*X+1)>>1.
> The above expression is quite unfamiliar to me... why +1 then >>1?
> '+1' is round up for fixed number by /2. There is because my CCS bad work with unsigned numbers, for next round up use bit 14.

> > Y=Y1*T will have 15 bit exactitude, scaler 128 in mind.
Must be Y=(Y1*T+0x4000)>>8;

> If you choose b=7, scaling 128, then the final result will be scaling
> 128*128=16384(14 bits), right?
As you see, b=8 for T & b=7 for result.
Sorry my bad hurry.

Cheers

Again bad hurry: shift rezult only >>8, thus Y=(T*X*T+0x100)>>9
Shame for me

Walala & all have read above: i am sorry & never shall write after birthday's wine.