How to do a frequency analysis of some velocity profiles?

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Hello

I have some question regarding analysing some post-processing data. I have extracted a linear and angular velocity of the robot moving around. The velocity is coming from AMCL and angular velocity is calculating with the help of IMU unit (just use the position/orientation) and AMCL as well. I made different bag files( so different robot runs) and I have significant peeks (noises) in both profiles( in linear velocity not so much noises bit the angular velocity have significant noises). So thought a frequency analysis of the velocity profiles might reveal more high components in both velocity profiles. But dont know exactly how to do it? Also where this noises can come from??

Im posting one of my profiles. Angular speed

And the linear one!!

This IS the code for the speed calculation

void speedCallback(const geometry_msgs::PoseWithCovarianceStamped::ConstPtr& msg)
{

    btScalar r,p,y;
    btQuaternion q(msg->pose.pose.orientation.x,msg->pose.pose.orientation.y,msg->pose.pose.orientation.z,msg->pose.pose.orientation.w);
    btMatrix3x3(q).getEulerYPR(y,p,r);
    std_msgs::Float64 yaw;
    yaw.data = y;

    if (count2 == 0){
        time_prev = ros::Time::now().toSec();
        count2=1;
    }

    double time_now = ros::Time::now().toSec();
    double curr_theta = yaw.data;
    double curr_x = msg->pose.pose.position.x;
    double curr_y = msg->pose.pose.position.y;

    if (curr_x < 0){
        curr_x = curr_x * -1;
    }
    if (curr_y < 0){
        curr_y = curr_y * -1;
    }
    double time_dif = time_now - time_prev;
    if (prev_x != 0 || prev_y != 0){
        if (time_dif != 0){
            double dist_theta = (curr_theta - prev_theta);
            if (dist_theta < 0){
                dist_theta = dist_theta * -1;
            }
            double dist_x = (curr_x - prev_x);
            if (dist_x < 0){
                dist_x = dist_x * -1;
            }
            double dist_y = (curr_y - prev_y);
            if (dist_y < 0){
                dist_y = dist_y * -1;
            }
            double dist_tot = sqrt((dist_x * dist_x) + (dist_y * dist_y));// * 10;
            double speed = (dist_tot / time_dif);// * 3.6;
            double speed_theta = dist_theta /time_dif;
            if (speed < 0.12){
                speed = 0;
                zero_count++;
            }
            if (speed_theta < 0.07){
                speed_theta = 0;
            }

            ROS_INFO("linear speed= %f, anglular speed=  %f", speed, speed_theta);
            myfile <<  speed << "   " << speed_theta << "\n";
            speed_count++;
            speed_sum = speed_sum + speed;
            speed_sum_theta = speed_sum_theta + speed_theta;
            if (speed_count == 20){
                speed = speed_sum / speed_count;
                speed_theta = speed_sum_theta / speed_count;
                if (zero_count > 7){
                    speed = 0;
                }
                speed_count = 0;
                speed_sum = 0;
                speed_sum_theta = 0;
                zero_count = 0;

                count = count + 1;
            }

        }
    }

    prev_theta = curr_theta;
    prev_x = curr_x;
    prev_y = curr_y;

    time_prev = time_now;

}

Frames.pdf