FIR filter design with time and frequency domain constraints I deal with the problem of the synthesis of the filter with the requirements of both the frequency and
time characteristics.

Now there is a filter that meets the requirements.
Roughly speaking the requirements are as follows:

Frequency response

FIR Low Pass


Fpass ~ 0.0(3) (* pi rad/sample)
Fstop ~ 0.1(6) (* pi rad/sample)
bandwidth irregularity of ~ 1e-3 (maybe ~ 1e-2) dB
~ -40 dB suppression


Time requirements


Overshoot in step response ~ 4% (transition time ~ 1e-2 ms)


I would like to know about the possibilities of such a synthesis (I’m with filterDesigner in the matlab failed, tried free tools - Iowa Hills)
or at least about the transformation of the finished filter into a narrower
(Fpass = 0.025, Fstop = 0.125) (Matlab can do this, but only IIR is obtained).
The most straightforward way to impose constraints in the frequency domain as well as in the time domain for the design of (linear phase) FIR filters is to use linear programming. 

Constraints on the step response or on the impulse response are naturally linear, and constraints on the frequency response can also be formulated as linear constraints in the case of linear phase FIR filters.

Take a look at this document for some examples. More details on the linear programming formulation of the FIR filter design problem can be found in this paper.